Our submissions for GD contests 1995-01

Transcription

U NIVERSITY
OF
L JUBLJANA
I NSTITUTE OF M ATHEMATICS , P HYSICS AND M ECHANICS
D EPARTMENT OF T HEORETICAL C OMPUTER S CIENCE
JADRANSKA 19, 1 000 L JUBLJANA , S LOVENIA
Preprint series, Vol. 40 (2002), 568/2
LAYOUTS FOR
GRAPH DRAWING CONTESTS
1995-2001
Vladimir Batagelj, Andrej Mrvar
ISSN 1318-4865
Version 1: May 13, 1998
Version 2: December 27, 2001
Math.Subj.Class.(2000): 05 C 90, 68 R 10, 76 M 27, 68 U 05,
05 C 50, 05 C 85, 90 C 27, 92 H 30, 92 G 30, 93 A 15, 62 H 30.
Supported by the Ministry of Education, Science and Sport of Slovenia,
Project J1-8532.
Address: Vladimir Batagelj, University of Ljubljana, FMF, Department
of Mathematics, and IMFM Ljubljana, Department of TCS, Jadranska
ulica 19, 1 000 Ljubljana, Slovenia
e-mail: vladimir.batagelj@uni-lj.si
Ljubljana, December 27, 2001
Layouts for
Graph Drawing Contests
1995-2001
Vladimir Batagelj
Department of Mathematics, University of Ljubljana
vladimir.batagelj@uni-lj.si
Andrej Mrvar
Faculty of Social Sciences, University of Ljubljana
andrej.mrvar@uni-lj.si
Graph drawing contests
Since 1994 graph drawing contests are organized as a part of the Graph Drawing Conferences. The rules and data are described on Internet and participants send their drawings
till the specified date. They can use any technique to get layouts of graphs. The primary
judging criterion is how well the drawings convey the information in the graphs: vertex
identifiers, vertex types, and vertex interconnectivity. A secondary criterion is the degree
to which manual editing was employed to produce the layout: the less manual intervention,
the better.
The purpose of the contests is to monitor and challenge the current state of the art in
graph-drawing technology.
Data (vertices and lines) for 3 or 4 graphs are given each year. A winning entry for each
graph is chosen by a panel of experts.
In this paper we collected our submissions to the contests in the years 1995–2001. They
are available also at
http://vlado.fmf.uni-lj.si/pub/gd/gd95.htm
and the original data (and their versions in Pajek format) at
http://vlado.fmf.uni-lj.si/pub/networks/data/gd/gd.htm
There you will find also pictures in some (dynamical) graphical formats (VRML, SVG) that
can not be adequately reproduced in the paper form.
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Layouts for Graph Drawing Contest 1995
In 1995 the Graph Drawing Conference was helt in Passau and the contest was organized
by Peter Eades and Joe Marks. Rules and data are described at:
http://www.uni-passau.de/agenda/gd95/contest.html
Graph A95
First layout was obtained automatically using our program COORD (positioning vertices on the rectangular net so that the number of crossings of lines is as low as
possible).
Manual editing was performed to reposition vertices using our graph picture editor
DRAW.
Graph B95
Analysing graph B using our program RELCALC two central vertices were found (1
and 34).
Feasible possitions for vertices were generated (two families of concentric circles).
Vertices 1 and 34 were fixed in the centre of the concentric circles mentioned.
Other vertices were automatically positioned around using program COORD so that
the total length of the lines was minimized.
Layout was then edited manually using DRAW to reposition vertices to minimize
crossings (concentric circles cannot be seen any more).
The layout was awarded the honorable mention.
Graph C95
First layout was obtained automatically using our program ENERG (minimisation of
ENERGy).
Some manual editing using DRAW was performed to reposition vertices.
The layout was awarded the first prize.
See: http://vlado.fmf.uni-lj.si/pub/gd/gd95.htm
The complete report of the contest is available in [6] and:
http://www.merl.com/reports/TR95-14/index.html
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Figure 1: Graph A95.
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MUX
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INSTRUCTION BUFFER (4 x 16)
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RCV
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DRV
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ROM REG
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MUX
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ROM ADDR
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MACRO INSTRUCTION ROM
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MUX
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L2
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MUX
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GENERAL REGISTER FILE (32 x 32)
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ALU
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A STAGE
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MUX
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L1
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MUX
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SHIFTER
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J REG
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PROGRAM COUNTER
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PSW SSW
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B STAGE
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C STAGE
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PIPELINE CONTROL
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OUTPUT
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ALIGN
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INPUT
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MUX
INSTRUCTION BUS INTERFACE
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MACRO INSTRUCTION UNIT
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ALU
INTEGER EXECUTION UNIT
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ACCUMULATOR
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INSTRUCTION CONTROL UNIT
FPU REGISTER FILE (8 X 64)
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ENCODER
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INSTRUCTION BUS TO I-CAMMU
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DATA BUS TO D-CAMMU
DATA BUS INTERFACE
FLOATING POINT UNIT
EXTERNAL
Figure 2: Graph A95 descriptions.
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Figure 3: Graph B95 (honorable mention).
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graphics.c:GRDisplayPoint
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X11/X.h:XID
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long1.c:GRDisplayPoint
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X11/Xlib.h:struct Xlib_h_57
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long2.c:GRDisplayPoint
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X11/Xlib.h:ScreenFormat
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short.c:GRDisplayPoint
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X11/X.h:GCFont
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X11/Xlib.h:Status
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gremlin.h:dby_to_win
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X11/X.h:GXxor
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X11/Xlib.h:XCharStruct
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X11/X.h:GCFunction
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X11/Xlib.h:XExtData
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X11/Xlib.h:XGCValues
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X11/X.h:KeySym
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gremlin.h:dbx_to_win
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X11/X.h:GContext
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graphics.c:text_pf
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X11/Xlib.h:Screen
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main.c:pix_gc
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X11/Xlib.h:XModifierKeymap
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main.c:display
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X11/Xlib.h:XFontProp
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X11/Xlib.h:XChangeGC
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<void>:struct _XrmHashBucketRec
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X11/Xlib.h:XCopyPlane
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<void>:struct _XKeytrans
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/usr/include/strings.h:strlen
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<void>:struct _XIMFilter
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main.c:Artmode
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<void>:struct _XExten
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main.c:SUN_YORIGIN
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<void>:struct _XContextDB
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main.c:SUN_XORIGIN
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<void>:struct _XFreeFuncs
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main.c:pix_sw
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<void>:struct _XSQEvent
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X11/Xlib.h:XDrawString
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<void>:struct _XDisplayAtoms
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/usr/include/stdio.h:sprintf
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icons/icon.littlepoint:littlepoint_pm
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X11/Xlib.h:struct _XExtData
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X11/Xlib.h:XFontStruct
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X11/Xlib.h:XPointer
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icondata.c:mpr_static
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gremlin.h:PMRec
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X11/Xlib.h:Display
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gremlin.h:FALSE
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X11/X.h:Atom
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X11/X.h:Window
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X11/Xlib.h:Depth
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X11/Xlib.h:GC
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X11/X.h:Colormap
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gremlin.h:struct PMRec
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X11/X.h:KeyCode
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X11/X.h:Font
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X11/Xlib.h:Visual
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X11/Xlib.h:struct _XDisplay
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X11/Xlib.h:Bool
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X11/Xlib.h:struct _XGC
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X11/X.h:VisualID
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X11/X.h:Pixmap
procedure
macro
type
variable
Figure 4: Graph B95 descriptions.
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Figure 5: Graph C95 (first prize).
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Figure 6: Graph C95 descriptions.
t-node
o-node
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In 1996 Graph Drawing Conference was helt in Berkeley, and the contest was organized by
Peter Eades, Joe Marks, and Stephen North. Rules and data are desribed at:
http://portal.research.bell-labs.com/orgs/ssr/people/
north/contest.html
Graph B96
First layout was obtained automatically using our program COORD. (positioning vertices on the rectangular net so that the number of crossings of lines is as low as
possible).
Manual editing was performed to reposition vertices using our graph picture editor
DRAW.
The layout was awarded the honorable mention.
Graph C96
Analysing graph C using our program RELCALC two parts and 2 connecting vertices
were found.
Each part was handled separately using our program ENERG (minimisation of energy). One part consists of a lattice structure, and the second of a planar graph of
cylindric symmetries. This spatial picture was realized in VRML (produced from the
description in our graph description language NetML based on SGML).
Some manual editing was done for planar representation.
Graph D96
Analysing graph D using program RELCALC 17 important vertices of ’kernel graph’
were found.
The first layout for these 17 vertices was obtained automatically using program COORD.
Other vertices were added to the obtained picture.
Some manual editing using DRAW was performed to reposition vertices to avoid crossings.
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Figure 7: Graph B96 (honorable mention).
See: http://vlado.fmf.uni-lj.si/pub/gd/gd96.htm
The complete report of the contest is available in [10] and:
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207-555
415-555
303-555
617-555
313-555
406-555
304-555
603-555
Figure 8: Graph B96 types.
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415-555-5266
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207-555-7281
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303-555-9878
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603-555-4321
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617-555-1958
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415-555-5058
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603-555-6565
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603-555-5694
Figure 9: Graph B96 labels.
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Figure 10: Graph C96 (first prize).
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Figure 11: Graph C96 / VRML snapshot.
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Figure 12: Graph C96 with cylinder / VRML snapshot.
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Figure 13: Graph D96.
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For Your Business
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label1
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Surfing for Savings?
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You Will
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http://www.att.com/easycommerce/images/w
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http://www.att.com/work/
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http://www.att.com/hr/employment/matrix.
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http://www.att.com/indiahorizons/connect
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http://www.att.com/youwill/
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http://www.att.com/images/ltbar2.gif
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Employment
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label2
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On The Go
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Write To Us
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http://www.att.com/images/attlogo-8hw.gi
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http://www.att.com/hr/
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http://www.att.com/hr/employment/prof_de
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http://www.att.com/onthego/
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Copyright
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http://www.att.com/news/../images/topnav
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800 number
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label3
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Now shipping: Windows NT developer’s kit
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AT&T WorldNet Service officially availab
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http://www.att.com/maps/topnav.map
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http://www.tollfree.att.net/dir800/
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http://www.att.com/hr/employment/support
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http://www.att.com/press/0396/960312.gba
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http://www.att.com/press/0396/960314.bsa
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http://www.att.com/news/images/newshead.
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News for the Month
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webmaster@att.com
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Business Network
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Calendar
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http://www.att.com/news/images/newsside.
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http://www.att.com/news/
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AT&T EasyLink Services (SM)
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http://www.att.com/bnet/
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http://www.att.com/easycommerce/easycomc
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http://www.att.com/news/images/newssub.g
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AT&T Corporate Server Team
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http://www.att.com/easycommerce/easylink
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AT&T Home Page
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Home
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http://www.att.com/news/images/newsheads
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http://www.att.com/homes/
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For Your Business
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AT&T Universal Card
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On The Net
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http://www.att.com/news/newsside.map
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Library
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Net
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http://www.att.com/ucs/
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On The Go
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http://www.att.com/images/hpbut20.gif
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http://www.att.com/library/
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AT&T/A-Z
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webmaster@att.com
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For Your Home
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http://www.mckinley.com/
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On The Net
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http://www.att.com/atoz
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AT&T/A-Z
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calling plan
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http://www.att.com/hr/employment/images/
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http://www.att.com/net/
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For Your Home
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Search
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http://www.att.com/true/truefacts.html
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http://www.att.com/hr/employment/nav.map
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Lucent Technologies
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http://www.att.com/home
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http://www.att.com/search.html
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Copyright
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http://www.att.com/images/index.gif
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http://www.att.com/lucent
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CNI to offer AT&T and Unisource voice an
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TrueVoice
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AT&T/A-Z
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Copyright
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http://www.att.com/press/0396/960313.bsa
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http://www.att.com/true/truevoice.html
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http://www.att.com/news/../atoz.html
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http://www.att.com/copyright.html
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Site Map
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On The Go
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webmaster@att.com
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AT&T - Employment Opportunities
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AT&T Home Page
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AT&T Easy World Wide Web (SM)
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Home Page
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Sonet T155 service gets first add/drop m
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http://www.att.com/images/homesolu.gif
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http://www.att.com/
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http://www.att.com/easycommerce/easywww
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http://www.att.com/index.html
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http://www.att.com/press/0396/960313.bsb
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http://www.att.com/images/athome.gif
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Site Map
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Search
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Thanks to the new telecommunications law
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http://www.att.com/indiahorizons/
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http://www.att.com/sitemap
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http://www.att.com/news/../search.html
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http://www.att.com/press/0296/960208.cha
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http://www.att.com/indiahorizons/images/
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http://www.att.com/images/truvoice.gif
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Conferences
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telemkt@attmail.com
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Write To Us
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http://www.att.com/indiahorizons/images/
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AT&T EasyCommerce Services
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http://www.att.com/news/conferences.html
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mailto:telemkt@attmail.com
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http://www.att.com/news/../write.html
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http://www.att.com/maps/index.map
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Work
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Write To Us
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Search
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http://www.att.com/net/yougotit.html
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http://www.att.com/infocenter/toc.html
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label0
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http://www.att.com/write/
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http://www.att.com/search/
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http://www.att.com/microscapes/microscap
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Globe
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Home Solutions
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Copyright
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http://www.att.com/net/yougotit.html/ima
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http://www.att.com/indiahorizons/home.ht
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http://www.att.com/providers
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http://www.att.com/home/homesol.html
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AT&T Corporate Server Team
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http://www.att.com/easycommerce/images/t
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http://www.att.com/easycommerce/whatsnew
29
webmaster@att.com
65
Copyright
101
webmaster@att.com
137
http://www.att.com/easycommerce/document
173
AT&T Home Page
30
mailto:webmaster@att.com
66
New U transceiver chips enable lower cos
102
Search
138
174
AT&T Newsroom
31
On The Net
67
http://www.att.com/press/0396/960312.mea
103
What’s New!
139
http://www.att.com/easycommerce/
175
http://www.att.com/maps/bar2.map
32
For Your Business
68
AT&T Global Alliance Marketing
104
http://www.att.com/whatsnew.html
140
http://www.att.com/images/bar.gif
176
AT&T at Home
33
Speeches Online
69
http://www.att.com/easycommerce/alliance
105
Site Map
141
http://www.att.com/maps/bar.map
177
You Got It.
34
http://www.att.com/news/speeches
70
For Your home
106
http://www.att.com/news/../sitemap.html
142
http://www.att.com/easycommerce/images/h
178
35
label0
71
InfoCenter
107
Index
143
http://www.att.com/easycommerce/home.map
179
AT&T India Horizons
36
http://www.att.com/hr/employment/overvie
72
http://www.att.com/infocenter
108
http://www.att.com/infocenter/attindex.h
144
http://www.att.com/easycommerce/images/m
180
http://www.att.com/press/
Figure 14: Graph D96 labels.
18
In 1997 Graph Drawing Conference was helt in Rome and the contest was organised by
Peter Eades, Joe Marks, and Stephen North. Rules and data are described at:
http://portal.research.bell-labs.com/orgs/ssr/people/
north/contest.html
Graph A97
First layout was obtained automatically using draw/eigenvalues option in program Pajek. Manual editing was used to reposition vertices in the grid to obtain
orthogonal layout in plane.
Manual editing in 3D was performed to get orthogonal embeddings in space: minimal, symmetric and cube.
Graph B97
Analysing graph B using our program MODEL we obtained (almost) regular partition
in 3 classes. The third class contains only vertex Harmony Central. The second
class, represented by squares, contains 11 vertices that are connected only to the
vertices in the class 1 (represented by circles). Vertices in class 1 are also connected
to other vertices in the same class. We first drew all vertices in the class 1 in the center
and vertices in class 2 separately – using class shrinking and circular drawing options
in Pajek. Afterward we manually moved vertices of class 1 connected to only one
vertex of class 2 close to this vertex. Finally we manually arranged the remaining
vertices of class 1.
We transformed given similarities on arcs to dissimilarities
and applied
Ward’s hierarchical clustering method to the obtained dissimilarity matrix. We produced a clustering into 12 clusters, shrank the graph using Pajek, and draw the obtained skeleton minimizing the number of crossings. Finally we manually arranged
the vertices of original graph.
See also
http://vlado.fmf.uni-lj.si/pub/gd/gd97.htm
The complete report is available in [7] or at
19
111
112
109
85
86
88
89
105
25
72
47
19
75
106
108
24
56
82
44
28
95
15
14
16
40
29
13
80
66
12
90
91
30
2
60
74
23
92
93
94
79
67
63
36
84
32
81
37
5
46
83
68
73
35
58
55
98
96
3
48
64
99
97
76
41
6
18
45
65
59
87
107
17
110
71
53
61
4
34
70
54
42
11
8
77
10
26
51
117
119
27
20
7
9
33
62
43
49
52
31
39
78
22
57
115
113
1
69
38
50
21
104
103
102
101
118
120
Figure 15: Graph A97 – orthogonal layout in plane (first prize).
100
114
116
20
Figure 16: Graph A97 – 3D minimal / VRML snapshot.
21
Figure 17: Graph A97 – 3D symmetric / VRML snapshot.
22
Figure 18: Graph A97 – 3D cube / VRML snapshot.
23
Musky Muskie Lure Components
Tackle Box Survival - Surface
Identifying Vegetation
Sandell & Associates Surface L
Netscape Navigator Family
Netscape Devedge: Courses & Co
Netscape Devedge: Library
INI International: Grocery Sec
Cold Front Tactics
Netscape Devedge: Library 1
Janet’s Horsin’ Around On The
Nada138-954
Intranet Executive: Digital Id
INI International: Vitamins
Designercity2
INI International: Candy Secti
Designercity5
Equinet(tm) - Comments
Boston At Night: Feature Story
The London College Of Fashion
404 Not Found
Wavelet Resources
Designercity4
Wavelet Netcare
Designercity1
Four Corners Hantavirus
Wavelab
Journal Entry
Designercity6
Designercity3
Designercity
Microsoft Netshow Events Calen
Celery
Young Designer Of The Month
Onions
Kasparov Vs. DeepBlue: The Rem
Musky Have Teeth
The Biting Truth
Virtual Sound Canvas Online
Microsoft Corporation Home Pag
Guest Essay: David Stork
Bunyaviridae
Edirol Online
IBM Corporation
Harmony Central: Midi Tools
1997 North American Gs Develop
Figure 19: Graph B97 – regular equivalence.
24
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+*-,+./&).10324245
Figure 20: Graph B97 – Dendrogram for Ward’s method.
25
1997 North American Gs Develop
Microsoft Corporation Home Pag
Edirol Online
IBM Corporation
Virtual Sound Canvas
Guest Essay: D. Stork
Kasparov Vs. DeepBlue
The London College Of Fashion
Microsoft Netshow Events Calen
Janet’s Horsin’ Around On The
Designercity4
Designercity
Designercity3
Designercity6
Designercity5
Designercity2
Designercity1
Wavelab
Wavelet Netcare
Netscape Devedge: Library 1
Wavelet Resources
The Biting Truth
Netscape Devedge: Library
Bunyaviridae
Young Designer Of The Month
Musky Have Teeth
Intranet Executive: Digital Id
Boston At Night: Feature Story
Cold Front Tactics
Journal Entry
Celery
Onions
Nada138-954
Equinet(tm) - Comments
Four Corners Hantavirus
Harmony Central: Midi Tools
404 Not Found
Netscape Navigator Family
Musky Muskie Lure Components
Identifying Vegetation
Sandell & Associates Surface L
Tackle Box Survival - Surface
INI International: Vitamins
INI International: Candy Secti
INI International: Grocery Sec
Figure 21: Graph B97 – Ward’s clustering (first prize).
26
In 1998 Graph Drawing Conference was helt in Montreal and the contest was organised by
Peter Eades, Joe Marks, Petra Mutzel, and Stephen North. Rules and data are described at:
http://gd98.cs.mcgill.ca/contest/
All work was done using our program package Pajek, which is freely available at:
http://vlado.fmf.uni-lj.si/pub/networks/pajek/
Graph A98
The data for graph A consist of addition and deletion operations that specify how the graph
changes over time. In our solution addition and deletion operations were performed using macro language which is recognized by program package Pajek. Then we used
Microsoft Camcorder (free software) to record the process. Selected layouts in three
different time points are shown.
Graph B98
Symmetries in graph (with some exceptions) can easily be noticed. We started the drawing using the layout obtained using Fruchterman-Reingold spring embedder. Later we used
manual editing to maximize symmetries and made some displacements according to different sizes and shapes of nodes. Pajek was used to do all the work.
Graph C98
Using spring embedders we could not get any nice layouts. Analysing graph we found that
it is a symmetric cubic graph. Later we used eigenvectors approach and computed eigenvectors of neighbourhood matrix that correspond to the largest eigenvalue (which is multiple).
In this way we got nice symmetric picture in space (3D). According to symmetries (equivalences) some of the nodes are drawn on the same positions and some are overlapping when
selecting the certain view to see the symmetries. Since some vertices are overlapping we
built a list of overlapping vertices drawn in different colors:
Graph D98
There were no data available for this graph. The participants could send any picture that
is inspired or related to graph drawing. We decided to generate graph from dictionary and
sent some interesting subgraph of it.
27
Table 1: Overlapping vertices in graph C98
Group
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
Color
Yellow
Green
Pink
Blue
Fuchsia
White
Orange
Purple
NavyBlue
TealBlue
OliveGreen
Gray
Black
Maroon
LightGreen
Cyan
Yellow
Green
Pink
Blue
Fuchsia
White
Orange
Purple
NavyBlue
TealBlue
OliveGreen
Gray
Black
Vertices
13, 76
9, 12, 33,106
39, 65, 88,112
5, 20, 51, 63
68, 75, 85, 92
36, 99
21, 42
23, 24, 55, 89
30, 44, 54, 57
3, 11, 43,101
1, 18, 64, 74, 91,103,104,107
19, 26, 47, 59
17, 40, 70, 79
48, 53
25, 32, 35, 60, 66, 71, 73,105
10,102
2, 22, 81, 90
14, 58, 61, 83
4, 15, 46, 52, 77, 78,109,110
7, 8, 27, 41
6, 50, 67, 96
82, 84, 95, 97
31, 80
16, 29, 98,108
38, 72, 86, 87
37, 45
28, 62, 93,111
34, 49, 56,100
69, 94
Large graph can be generated from words in a dictionary. We constructed a graph in
which two words are connected iff one can be obtained from the other by changing single character (e. g. WORK – WORD) or by adding/deleting one character (e.g. EVER
– FEVER). Then we took english words graph-drawing-contest, find all shortest paths between graph and drawing and between drawing and contest, draw
the obtained graph using layers option in Pajek (layers are determined by distance from
drawing). Additionally we added two puzzles:
one difficult: find shortest paths alone,
28
Figure 22: Graph C98.
one easy: find only missing words on the paths.
See also: http://vlado.fmf.uni-lj.si/pub/gd/gd98.htm
Figure 23: Graph A98, after executing deletion:
delete www.att.com -> www.att.com/catalog/consumer
(23 operations executed).
www.att.com/cgi-bin/ppps.cgi
www.att.com/write
www.att.com/textindex.html
www.att.com/cmd/custcare
www.att.com/cmd/jump
www.att.com/home
www.att.com/bmd/jump
search.att.com
www.att.com
www.att.com/bmd/tollfree
www.att.com/worldnet
www.att.com/worldnet/wmis
www.att.com/catalog/consumer
www.att.com/whatsnew
www.att.com/catalog/small_business
www.att.com/terms.html
www.att.com/cgi-bin/bmd_cart.cgi
www.att.com/features
www.att.com/rock
www.att.com/catalog
www.att.com/att
www.att.com/learningnetwork
29
www.att.com/write
www.att.com/bmd/products
search.att.com
www.att.com
www.att.com/home
www.att.com/worldnet/intranet
www.att.com/net
www.att.com/worldnet/wis/sky/signup.html
www.att.com/news
www.att.com/services
www.att.com/rock
www.att.com/catalog
www.att.com/att
30
Figure 24: Graph A98, after executing deletion:
delete www.att.com/whatsnew -> www.att.com/catalog/consumer
(38 operations executed).
Figure 25: Graph A98, after all additions/deletions done (65 operations executed).
www.catalog.att.com/cmd/jump
www.att.com/write
www.att.com/bmd/products
www.att.com/cgi-bin/cart.cgi
www.att.com/cmd/products
search.att.com
www.att.com/cmd/custcare
www.att.com/cmd
www.att.com
www.att.com/bmd/tollfree
www.att.com/home
www.att.com/worldnet/intranet
www.att.com/business
www.att.com/net
www.att.com/worldnet/wis/sky/signup.html
www.att.com/news
www.att.com/bmd/custcare
www.att.com/speeches
www.att.com/speeches/index96.html
www.att.com/services
www.att.com/catalog
www.att.com/international
www.att.com/rock
www.att.co.uk
www.att.com/att
www.att.com/learningnetwork
31
Tag 5
Tag 1
1
2
Tag 31
Tag 58
Tag 54
1
6
Tag 2
0
Tag 3
14F
1
3
1
Tag 29
Tag 6
2
Figure 26: Graph B98 (first prize).
Tag 30
1
Tag 57
1A
Tag 49
Tag 74
Tag 55
Tag 35
Tag 43
Tag 17
Tag 41
1
Tag 44
3H
11
Tag 67
1
Tag 34
1
Tag 40
Tag 36
5
Tag 64
12
Tag 45
Tag 4
13
3
Tag 33
Tag 65
Tag 63
Tag 51
Tag 50
Tag 71
Tag 56
4
2
Tag 59
Tag 32
15
4H
Tag 73
1A
Tag 39
Tag 60
Tag 70
Tag 48
Tag 37
Tag 61
1A
Tag 14
Tag 47
Tag 46
Tag 9
1
Tag 7
2
1
Tag 13
Tag 12
3
Tag 15
1
Tag 16
Tag 8
Tag 11
3H
4H
1
Tag 10
2
Tag 66
Tag 42
Tag 68
Tag 69
Tag 75
2A
10
Tag 72
Tag 38
7
2A
Tag 18
Tag 26
Tag 25
1
Tag 27
9
Tag 28
Tag 53
2A
Tag 62
Tag 22
Tag 52
1
Tag 24
8
1
Tag 20
Tag 21
Tag 19
Tag 23
32
drawing
Figure 27: Graph D98: Difficult puzzle.
graph
contest
Pajek
33
drawing
draping
craping
crating
raping
rating
aping
Figure 28: Graph D98: Easy puzzle.
grating
gratin
pine
pipe
grates
graph
cong
ripe
grate
graphs
pong
grape
gripe
rape
cove
covet
cover
covert
convent
content
contest
Pajek
34
drawing
draping
craping
crating
raping
rating
aping
Figure 29: Graph D98: Solution.
grating
ping
gratin
pine
gratis
pipe
grates
cong
ripe
grapes
grate
graphs
grape
graph
pong
gripe
cone
rape
cove
covet
cover
covert
convert
convent
content
contest
Pajek
35
36
In 1999 Graph Drawing Conference was helt in Stirin (Czeck Republic) and the contest
was organised by Franz Brandenburg, Michael Juenger, Joe Marks, Petra Mutzel, and Falk
Schreiber. Rules and data are described at:
http://www.ms.mff.cuni.cz/acad/kam/conferences/GD99/
contest/rules.html
All work was done using our program package Pajek, which is freely available at:
http://vlado.fmf.uni-lj.si/pub/networks/pajek/
Graph A99
Graph data were transformed to Pajek format, which enables to handle graph changes over
time. The following coding of actors is used:
Shapes
– circle: =f= female
– triangle: =m= male
– yellow box: =b= female+male (Ernst+Lisl Wiesenhuber)
– green box: =a= women+grandchildren (Julia von der Marwitz)
– black diamond: =w= widowed
– pink diamond: =d= divorced marriage
– orange diamond: =m= still existing marriage
– empty: =i= invisible node (white)
Sizes
– 0.8 - big
– 0.4 - small
– 0.6 - artificial
Colors
– =y= unactive characters (yellow)
– =a= 2 persons in 2 different colors (green)
– =b= active characters (blue)
– =d= divorced marriage (pink)
37
– =w= characters that never showed up personally (white)
– =m= still existing marriage (orange)
– =g= already dead characters (grey)
– =w= widowed (black)
Border widths
– =p= picture - border width = 2
– =s= symbol - border width = 0.5
Drawing of the current situation We started the drawing using the layout obtained
by Kamada-Kawai spring embedder. Later we used manual editing to arrange them on
rectangular net.
Development of the graph over time We used the Pajek option for drawing graphs
in different time points. Only time points where at least one vertex or one line changes
according to last layout were drawn (e.g. 1, 2, 4, 5,...). After each change time the layout of
the new graph was optimized starting with the previous positions.
Graph B99
We used eigenvectors approach and computed eigenvectors of Laplacean matrix that correspond to the 1st, 2nd and 5th largest eigenvalue. No additional manual editing was used on
the obtained spatial picture. Suitable view was selected to get planar EPS picture. Picture
was exported to formats for the following 3D viewers: VRML (CosmoPlayer), kinemages
(Mage), and MDLMOLfile (Chime).
The layout was awarded the second prize.
Graph C99
We started the drawing using the layout obtained by Fruchterman-Reingold spring embedder. Later we used manual editing to maximize ’rectangularity’ and made some displacements to accommodate for different sizes of nodes.
See: http://vlado.fmf.uni-lj.si/pub/gd/gd99.htm .
The complete report of the contest is available in [8].
Dr. Eva-Maria Sperling
*06.08.1947
Momo Sperling
*01.04.1975
Rita Bassermann
*22.05.1962
Gundel Koch
Professor Dr. Rudolf Tenge-Wegemmann
*1947+1964
Elena Sarikakis
*08.11.1939
Vasily Sarikakis
*14.02.1963
Hilmar Eggers
Frau Horowitz
Simone Fitz
Ernst+Lisl Wiesenhuber
Dr. Ludwig Dressler
*27.06.1933
Chromo Hoyonda
*25.10.1970
*26.11.1987+18.08.1996
Figure 30: Graph A99, current situation.
*18.07.1996
Zeki Kurtalan
Sue
Sarah Ziegler
*22.10.1987
Fritjof
Lothar Boedefeld
*06.04.1940
Berta Griese
geb.Nolte*25.06.1941
Mary Kling
geb.Dankor*30.01.1969
Andy Zenker
*03.07.1947
Rolf Sattler
*14.11.1991
Inge Kling
Harry
Hajo Scholz
*09.06.1944
Bolle Guenther Bollmann
Anna Ziegler
geb.Jenner*14.07.1959
Sophie Ziegler
*25.07.1991
*1955+1965
Gabi Zenker-geb.Skawowski
verw.Zimmermann*23.05.1960
Gung Pahm Kien
*23.10.1958
Irina Winicki
*18.10.1990
Pat Wolffson
*05.05.1972
Lisa Hoffmeister
*19.10.1981
Fausto Rossini
Dr. Otto Pichelsteiner
*10.05.1968+29.08.1991
Zorro Franz Josef Pichelsteiner
*09.08.1963
Philipp Sperling
*14.09.1977
Herr Panowski
Nico Zenker
*12.05.1994
Rosi Koch
gesch.Skabowski*19.10.1927
Martha
Hans Beimer
*03.10.1943
Marion Beimer
*21.05.1969
Marlene Schmitt
*02.07.1942
Wanda Winicki
geb.Kollin*17.07.1938
*30.01.1992
Tom Ziegler
*27.07.1989
Theresa Zenker
+1986
Friedemann Traube
Tanja Schildknecht-Dressler
geb.Schildknecht*19.06.1970
Phil Seegers
*14.04.1961
Dora Wittich
+1964
Beate Sarikakis
geb.Floeter*17.08.1970
*13.03.1994
Hans Wilhelm Huelsch
*29.02.1952
Olaf Kling
*10.11.1955
Frank Dressler
*31.10.1966
Isolde Pavarotti
verw.Panowak*27.11.1936
Alfredo
Francesco
Bruno Skabowski
Kaethe Georg Eschweiler
Dani Schmitz
Iffi Zenker
*19.08.1978
Klaus Beimer
*17.10.1078
*1969+1986
Olli Klatt
*06.01.1976
Valerie Ecker
geb.Zenker*08.10.1975
Canan Dagdelen
Helga Beimer Schiller
geb.Wittich*24.03.1940
Onkel Franz Franz Wittich
*24.07.1913
Carsten Floeter
*05.03.1966
*24.07.1997
Theo Klages
Leo Klamm
Erich-Schiller
*23.07.1944
Marcella Varese
Wilhelm Loesch
*19.09.1996
Else Kling
*14.05.1922
Unbekannter_Russe
Urzula Wienicki
*10.02.1963
*19.04.1996
Boris Ecker
*17.06.1965
Dr. Ahmet Dagdelen
Paula Madalena Francesca Winicki
*29.08.1996
Paolo Varese
Gina Varese
Winifred Snyder
Giovanna Varese
38
39
Sigi Kronmayr
Vasily Sarikakis
Hans Beimer
Marion Beimer
Else Kling
Elfie Kronmayr
Klaus Beimer Benny Beimer
Egon Kling
Gung Pahm Kien
Paul Nolte
Joschi Bennarsch
Berta Griese
Lydia Nolte
Chris Barnsteg
Dr. Ludwig Dressler
Theo Nolte
Franz Schildknecht
Philo Bennarsch
Henny Schildknecht
Stefan Nossek
Sigi Kronmayr
Herr Floether
Der Englaender
Vasily Sarikakis
Elisabeth Dressler
Elfie Kronmayr
Hans Beimer
Marion Beimer
Else Kling
Carsten Floeter
Egon Kling
Gung Pahm Kien
Paul Nolte
Joschi Bennarsch
Berta Griese
Lydia Nolte
Chris Barnsteg
Dr. Ludwig Dressler
Theo Nolte
Franz Schildknecht
Philo Bennarsch
Gottlieb Griese
Henny Schildknecht
Stefan Nossek
Sigi Kronmayr
Herr Floether
Der Englaender
Vasily Sarikakis
Elisabeth Dressler
Elfie Kronmayr
Marion Beimer
Else Kling
Carsten Floeter
Hans Beimer
Egon Kling
Gung Pahm Kien
Paul Nolte
Berta Griese
Lydia Nolte
Chris Barnsteg
Dr. Ludwig Dressler
Theo Nolte
Franz Schildknecht
Gottlieb Griese
Frank Dressler
Joschi Bennarsch
Meike Schildknecht Philo Bennarsch
Henny Schildknecht
Stefan Nossek
Figure 31: Graph A99, time points 5, 6 and 7 (first prize).
15241
15238
15244
15232
15148
15235
Figure 32: Graph B99 (second prize).
15220
15196
15229
15223
15217
15145
15193
15247
15199
15151
15139
15214
15226
15211
15187
15190
15127
15142
15175
15136
15208
15184
15178
15124
15172
15202
15130
15100
15154
15250
15106
15181
15118
15121
15169
15103
15094
15133
15205
15166
15082
15097
15115
15091
15163
15109
15085
15157
15079
15088
15253
15112
15073
15076
15160
15070
15256
15259
40
41
Figure 33: Graph B99 – general view.
42
Figure 34: Graph B99 – different views.
PROLINE
HYDROXYPROLINE
GLUTAMATE
ORNITHINE
5-AMINOLEVULINATE
PROTOPORPHYRIN IX
HEME
CHLOROPHYLL
CYTOCHROMES
COBALAMIN
2-OXOGLUTERATE
SUCCINATE
UREA
CYSTEINE
BILE PIGMENTS
Degradation
FUMARATE
ARGININE
GLYOXYLATE
CITRATE
METHIONINE
THREONINE
OXALOACETATE
ASPARTATE
Figure 35: Graph C99.
ALANINE
ACETYL-CoA
PYRUVATE
LEUCINE
VALINE
PHOSPOLIPIDS
BILE ACIDS
SUCROSE
ISOPRENOIDS
PENTOSES
GLYCOGEN
URONIC ACIDS
NDPGLUCOSE
STARCH
DEOXYRIBONUCLEIC ACID
3-P GLYCERATE
CYTIDINE NUCLEOTIDE
DEOXYCYTIDINE NUCLEOTIDE
GLYCINE
GLYCEROL
FATTY ACIDS
PLANT STEROIDS
DEOXYURIDINE NUCLEOTIDE
DEOXYTHYMIDINE NUCLEOTIDE
ISOLEUCINE
SERINE
STEROID HORMONES
URIDINE NUCLEOTIDE
RIBONUCLEIC ACID
TRIACYLGLYCEROLS
CHOLESTEROL
LYSINE
FRUCTOSE
AMINO SUGARS
FRUCTOSE 6-P
ASCORBATE
TYROSINE
GLYCERALDEHYDE 3-P
PHENYLALANINE
ERYTHROSE 4-P
GLUCOSE 6-P
RIBOSE 5-P
GLUCOSE
P-RIBOSYLPP
CELLULOSE
DEOXYADENOSINE NUCLEOTIDE
ADENOSINE NUCLEOTIDE
RIBONUCLEIC ACID
DEOXYGUANOSINE NUCLEOTIDE
GUANOSINE NUCLEOTIDE
HORMONES
INOSINE NUCLEOTIDE
CHORISMATE
LIGNIN
TRYPTOPHAN
HISTIDINE
NAD+
Degradation
XANTHOSINE NUCLEOTIDE
43
PROLINE
HYDROXYPROLINE
GLUTAMATE
ORNITHINE
5-AMINOLEVULINATE
PROTOPORPHYRIN IX
HEME
CHLOROPHYLL
CYTOCHROMES
COBALAMIN
Figure 36: Graph C99 - orthogonal layout.
2-OXOGLUTERATE
SUCCINATE
BILE PIGMENTS
Degradation
FUMARATE
ARGININE
GLYOXYLATE
CITRATE
UREA
CYSTEINE
METHIONINE
THREONINE
OXALOACETATE
ASPARTATE
ALANINE
ACETYL-CoA
LEUCINE
VALINE
PHOSPOLIPIDS
CHOLESTEROL
BILE ACIDS
PLANT STEROIDS
ISOPRENOIDS
PENTOSES
GLYCOGEN
URONIC ACIDS
DEOXYTHYMIDINE NUCLEOTIDE
3-P GLYCERATE
CYTIDINE NUCLEOTIDE
DEOXYCYTIDINE NUCLEOTIDE
GLYCINE
GLYCEROL
FATTY ACIDS
NDPGLUCOSE
STARCH
DEOXYURIDINE NUCLEOTIDE
ISOLEUCINE
SERINE
STEROID HORMONES
URIDINE NUCLEOTIDE
RIBONUCLEIC ACID
TRIACYLGLYCEROLS
CELLULOSE
LYSINE
PYRUVATE
FRUCTOSE
AMINO SUGARS
FRUCTOSE 6-P
ASCORBATE
TYROSINE
PHENYLALANINE
ERYTHROSE 4-P
GLUCOSE 6-P
RIBOSE 5-P
GLUCOSE
P-RIBOSYLPP
SUCROSE
DEOXYADENOSINE NUCLEOTIDE
ADENOSINE NUCLEOTIDE
RIBONUCLEIC ACID
DEOXYGUANOSINE NUCLEOTIDE
GUANOSINE NUCLEOTIDE
HORMONES
GLYCERALDEHYDE 3-P
INOSINE NUCLEOTIDE
CHORISMATE
LIGNIN
TRYPTOPHAN
HISTIDINE
NAD+
Degradation
XANTHOSINE NUCLEOTIDE
44
45
In 2000 Graph Drawing Conference was helt in Colonial Williamsburg (USA) and the contest was organised by Franz Brandenburg. Rules and data are described at:
http://www.infosun.fmi.uni-passau.de/GD2000/index.html
Graph A00
Graph A00 was proposed by M. Himsolt.
First we found out that graph consists of 26 weakly connected components. After removing loops from the graph we got acyclic graph. On the acyclic graph we used standard
algorithms to compute layers and position vertices into layers in order to minimize total
length of lines. Some manual repositioning of vertices was used to avoid some line crossings. Vertices having loops are drawn as ellipses other as rectangles. Since graph consists of
several components and labels are very small, some additional layouts of parts of network
(top, middle and bottom) containing some components are shown.
We also produced pictures of this graph in Scalable Vector Graphics (SVG) format
besides EPS pictures (see http://vlado.fmf.uni-lj.si/pub/gd/gd00.htm).
Graph B00
Graphs B00-A and B00-B were proposed by Ulrik Brandes.
The essential part of both graphs A and B are the green vertices. But there are to many
arcs among them to produce a clear picture.
We first tried with circular presentation. To reveal internal structure of green subgraph
on the green suband to determine the ordering of vertices on the circle we computed
graph and applied TSP (Travelling Salesman Problem) algorithm on this matrix.
'¡
Y¡3¢ £ ¤N¥§¦¨ © ª ¢ ¢ ££¦+¦+«¬ ª ¢ ¢ ¥§¥§¦¦ ©
(1)
©ª
ª ©
ª ¢ ¥§¦ is the neighborhood of vertex ¥®°¯ :
ª ¢ ¥¦²±£³³¯´¢ ¥®´-£¦µ>¶¸·
«
¬
( denotes the symmetric difference, denotes union)
Since there can exist different clusters inside the green set of vertices we extended the
H¡ matrix
with some additional vertices with equal distance to all green vertices. Some
vertices were repositioned manually according to connections to yellow and blue vertices
on the circular net. From obtained pictures we can see that neighbouring vertices have
similar patterns of arcs. Vertices having loops are drawn as boxes (vertices 5 and 11 in
graph A) other as circles. Different gray colors are used to show the frequency of contact:
46
Black: 1 - weekly
75% Gray: 2 - biweekly
50% Gray: 3 - monthly
25% Gray: 4 - quarterly
The ordering of green vertices obtained by TSP algorithm we used also in matrix representation of graphs A and B. It seems that the matrix representation is more appropriate for
dense (parts of) graphs. In the matrix representation the same shadowing is used as in the
graph layout.
The complete report of the contest is available in [9].
ConcretePrimitiveQuery
EntitiesByTypeQuery
PrimitiveQuery
RelationsByTypeQuery
SerialQuery
Block
list<STD_Ptr<Block>, allocator<STD_Ptr<Block>>>
ParallelQuery
RecursiveQuery
Scope
NameSpace
TemplateParameter
Template
Constant
list<ColumnDef, allocator<ColumnDef>>
list<Query*, allocator<Query*>>
Query
STD_Ptr<Block>
allocator<STD_Ptr<Block>>
iterator
STD_Ptr<Block>
multiset<STD_Ptr<Entity>, LessByName, allocator<STD_Ptr<Entity>>>
_Tree<STD_Ptr<Entity>, value_type, _Kfn, LessByName, allocator<STD_Ptr<Entity>>>
set<STD_Ptr<Scope>, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>>
_Tree<STD_Ptr<Scope>, value_type, _Kfn, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>>
ColumnDef
iterator
allocator<ColumnDef>
iterator
allocator<Query*>
Object
const_iterator
const_iterator
const_iterator
allocator<STD_Ptr<Entity>>
iterator
allocator<STD_Ptr<Scope>>
iterator
const_iterator
const_iterator
Routine
Field
Entity
DummyRelation
LocallyUsedType
StaticDataMemberTemplate
FunctionTemplate
ClassTemplate
Method
Function
Variable
Member
Accessor
Call
FieldAccess
Inheritance
TemplateInstance
LocalVariableOfType
HasType
Parameter
TypeUsedInTypeRef
ReturnType
Friend
Element
Relation
Type
SCPos
Builtin
RoutineType
TypeRef
Record
Pointer
TypeDef
Array
PointerToMember
QualifiedType
Union
Class
Struct
InScope
InNamespace
InRecordScope
Figure 37: Complete layout of Himsolt graph A00.
_Tree<string, value_type, _Kfn, less<string>, allocator<int>>
_Tree<string, value_type, _Kfn, less<ILInstanceKey>, allocator<int>>
_Tree<string, value_type, _Kfn, less<PropertyName>, allocator<int>>
Measurement
iterator
const_iterator
iterator
iterator
iterator
allocator<int>
map<string, int, less<ILInstanceKey>, allocator<int>>
value_compare
iterator
map<string, int, less<PropertyName>, allocator<int>>
value_compare
map<string, int, less<string>, allocator<int>>
value_compare
Log
map<int, string, less<int>, allocator<string>>
_Tree<PropertyName, value_type, _Kfn, less<string>, allocator<string>>
_Tree<string, value_type, _Kfn, less<string>, allocator<string>>
map<string, string, less<string>, allocator<string>>
_Tree<int, value_type, _Kfn, less<int>, allocator<string>>
value_compare
iterator
iterator
value_compare
iterator
iterator
allocator<string>
iterator
iterator
iterator
const_iterator
const_iterator
set<string, less<string>, allocator<string>>
Project
list<string, allocator<string>>
iterator
map<string, SourceFile, less<string>, allocator<SourceFile>>
value_compare
set<PropertyName, less<string>, allocator<string>>
CppModel
Model
ElementType
_Tree<string, value_type, _Kfn, less<string>, allocator<SourceFile>>
list<Relation*, allocator<Relation*>>
set<ElementType*, less<ElementType*>, allocator<ElementType*>>
const_iterator
allocator<SourceFile>
iterator
const_iterator
iterator
const_iterator
allocator<Relation*>
allocator<ElementType*>
_Tree<ElementType*, value_type, _Kfn, less<ElementType*>, allocator<ElementType*>>
iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<ElementType*>>
iterator
map<string, ElementType*, less<string>, allocator<ElementType*>>
value_compare
const_iterator
const_iterator
iterator
iterator
_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<PropertyName>>
_Tree<PropertyName, value_type, _Kfn, less<string>, allocator<PropertyName>>
set<PropertyName, less<string>, allocator<PropertyName>>
const_iterator
iterator
iterator
const_iterator
iterator
set<PropertyName, less<PropertyName>, allocator<PropertyName>>
_Tree<int, value_type, _Kfn, less<int>, allocator<PropertyName>>
UnimportantOperationException
allocator<PropertyName>
iterator
iterator
map<int, string, less<int>, allocator<PropertyName>>
value_compare
ParentScopeNotFoundException
UnimportantStatementException
BuildException
list<string, allocator<PropertyName>>
const_iterator
iterator
BrokenRelationException
map<ILInstanceKey, ILInstance, less<string>, allocator<ILInstance>>
EntryNotFoundException
_Tree<ILInstanceKey, value_type, _Kfn, less<string>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<PropertyName>, allocator<ILInstance>>
value_compare
iterator
iterator
_Tree<ILInstanceKey, value_type, _Kfn, less<ILInstanceKey>, allocator<ILInstance>>
ILManager
map<ILInstanceKey, ILInstance, less<ILInstanceKey>, allocator<ILInstance>>
map<ILInstanceKey, ILInstance, less<PropertyName>, allocator<ILInstance>>
allocator<ILInstance>
iterator
const_iterator
iterator
value_compare
value_compare
iterator
_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<Property>>
map<PropertyName, Property, less<PropertyName>, allocator<Property>>
allocator<BaseClass*>
list<BaseClass*, allocator<BaseClass*>>
iterator
allocator<Property>
const_iterator
iterator
value_compare
const_iterator
stack<Block*, deque<Block*, allocator<Block*>>>
deque<Block*, allocator<Block*>>
iterator
const_iterator
allocator<Block*>
_Tree<void*, value_type, _Kfn, less<void*>, allocator<Entity*>>
_Tree<void*, value_type, _Kfn,
less<void*>, allocator<Entity*>>
iterator
ProjectFile
map<string, SectionContents, less<string>, allocator<SectionContents>>
iterator allocator<Entity*>>
map<void*, Entity*, less<void*>,
list<Entity*, allocator<Entity*>>
_Tree<string, value_type, _Kfn, less<string>, allocator<SectionContents>>
list<TempResult, allocator<TempResult>>
set<STD_Ptr<Cell>, CellLessByElementID, allocator<STD_Ptr<Cell>>>
_Tree<STD_Ptr<Cell>, value_type, _Kfn, CellLessByElementID, allocator<STD_Ptr<Cell>>>
iterator
const_iterator
iterator
const_iterator
allocator<Entity*>
value_compare
value_compare
allocator<SectionContents>
iterator
allocator<TempResult>
iterator
allocator<Entity*>
iterator
const_iterator
const_iterator
const_iterator
TempResult
allocator<STD_Ptr<Cell>>
allocator<Element*>
list<Element*, allocator<Element*>>
iterator
const_iterator
allocator<Actual>
list<Actual, allocator<Actual>>
iterator
const_iterator
allocator<Constant*>
list<Constant*, allocator<Constant*>>
iterator
_Tree<TypeRefHack, value_type, _Kfn, LessByReferencedType, allocator<TypeRefHack>>
iterator
multiset<TypeRefHack, LessByReferencedType, allocator<TypeRefHack>>
allocator<TypeRefHack>
iterator
basic_string<char, char_traits<char>, allocator<char>>
allocator<char>
const_iterator
const_iterator
STD_Ptr<TemplateParameter>
list<STD_Ptr<TemplateParameter>, allocator<STD_Ptr<TemplateParameter>>>
iterator
const_iterator
allocator<STD_Ptr<TemplateParameter>>
CppModelFactory
codecvt<wchar_t, char, mbstate_t>
codecvt<char, char, state_type>
num_put<char, _Iter>
codecvt_base
numpunct<char>
failure
ModelFactory
multiset<RoutineTypeHack, LessByParamTypes, allocator<RoutineTypeHack>>
_Tree<RoutineTypeHack, value_type, _Kfn, LessByParamTypes, allocator<RoutineTypeHack>>
allocator<RoutineTypeHack>
iterator
const_iterator
facet
_Locimp
underflow_error
range_error
overflow_error
length_error
out_of_range
invalid_argument
domain_error
__non_rtti_object
runtime_error
vector<_Bool, _Bool_allocator>
reference
bad_cast
bad_alloc
logic_error
reverse_iterator<iterator, value_type, reference, reference*, difference_type>
const_iterator
reverse_iterator<const_iterator, value_type, const_reference, const_reference*, difference_type>
exception
bad_exception
bad_typeid
iterator
iterator
_Tree<Cell*, value_type, _Kfn, less<Cell*>, allocator<Cell*>>
map<Cell*, Cell*, less<Cell*>, allocator<Cell*>>
value_compare
allocator<Cell*>
list<Cell*, allocator<Cell*>>
const_iterator
iterator
iterator
const_iterator
SectionNotFound
FileNotInProject
FileException
VariableNotFound
Property
PropertyValue
Exception
list<PropertyValue, allocator<PropertyValue>>
basic_streambuf<char, char_traits<char>>
basic_istream<wchar_t, char_traits<wchar_t>>
const_iterator
locale
basic_ostream<wchar_t, char_traits<wchar_t>>
basic_fstream<char, char_traits<char>>
iterator
allocator<PropertyValue>
basic_filebuf<char, char_traits<char>>
basic_ios<wchar_t, char_traits<wchar_t>>
ios_base
basic_ostream<char, char_traits<char>>
basic_iostream<char, char_traits<char>>
basic_istream<char, char_traits<char>>
basic_streambuf<wchar_t, char_traits<wchar_t>>
basic_ios<char, char_traits<char>>
47
ConcretePrimitiveQuery
ColumnDef
EntitiesByTypeQuery
PrimitiveQuery
RelationsByTypeQuery
SerialQuery
list<ColumnDef, allocator<ColumnDef>>
iterator
const_iterator
allocator<ColumnDef>
list<Query*, allocator<Query*>>
iterator
const_iterator
ParallelQuery
allocator<Query*>
Query
RecursiveQuery
Object
STD_Ptr<Block>
Block
list<STD_Ptr<Block>, allocator<STD_Ptr<Block>>>
iterator
const_iterator
STD_Ptr<Block>
Figure 38: Upper part of Himsolt graph A00.
multiset<STD_Ptr<Entity>, LessByName, allocator<STD_Ptr<Entity>>>
Scope
_Tree<STD_Ptr<Entity>, value_type, _Kfn, LessByName, allocator<STD_Ptr<Entity>>>
set<STD_Ptr<Scope>, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>>
NameSpace
allocator<STD_Ptr<Entity>>
iterator
const_iterator
allocator<STD_Ptr<Scope>>
TemplateParameter
iterator
Template
const_iterator
_Tree<STD_Ptr<Scope>, value_type, _Kfn, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>>
Constant
Routine
Field
Entity
DummyRelation
LocallyUsedType
Accessor
Element
Call
FieldAccess
Relation
Inheritance
TemplateInstance
LocalVariableOfType
HasType
Parameter
TypeUsedInTypeRef
StaticDataMemberTemplate
ReturnType
FunctionTemplate
Friend
ClassTemplate
Method
Function
Variable
Member
Type
SCPos
Builtin
RoutineType
TypeRef
Record
Pointer
TypeDef
Array
InScope
PointerToMember
QualifiedType
Union
Class
Struct
InNamespace
InRecordScope
48
iterator
map<string, int, less<ILInstanceKey>, allocator<int>>
Measurement
map<string, int, less<PropertyName>, allocator<int>>
map<string, int, less<string>, allocator<int>>
const_iterator
iterator
iterator
iterator
allocator<int>
value_compare
iterator
value_compare
value_compare
Log
map<int, string, less<int>, allocator<string>>
value_compare
iterator
iterator
map<string, string, less<string>, allocator<string>>
value_compare
Figure 39: Middle part of Himsolt graph A00.
iterator
iterator
const_iterator
allocator<string>
iterator
iterator
const_iterator
iterator
set<string, less<string>, allocator<string>>
Project
list<string, allocator<string>>
map<string, SourceFile, less<string>, allocator<SourceFile>>
set<PropertyName, less<string>, allocator<string>>
iterator
const_iterator
value_compare
_Tree<string, value_type, _Kfn, less<string>, allocator<SourceFile>>
CppModel
Model
list<Relation*, allocator<Relation*>>
iterator
const_iterator
iterator
const_iterator
ElementType
allocator<Relation*>
set<ElementType*, less<ElementType*>, allocator<ElementType*>>
_Tree<ElementType*, value_type, _Kfn, less<ElementType*>, allocator<ElementType*>>
iterator
const_iterator
iterator
map<string, ElementType*, less<string>, allocator<ElementType*>>
value_compare
const_iterator
iterator
iterator
const_iterator
iterator
iterator
const_iterator
set<PropertyName, less<string>, allocator<PropertyName>>
iterator
set<PropertyName, less<PropertyName>, allocator<PropertyName>>
allocator<PropertyName>
iterator
iterator
map<int, string, less<int>, allocator<PropertyName>>
value_compare
UnimportantOperationException
ParentScopeNotFoundException
UnimportantStatementException
list<string, allocator<PropertyName>>
const_iterator
BuildException
iterator
BrokenRelationException
map<ILInstanceKey, ILInstance, less<string>, allocator<ILInstance>>
value_compare
EntryNotFoundException
iterator
iterator
allocator<ILInstance>
ILManager
map<ILInstanceKey, ILInstance, less<ILInstanceKey>, allocator<ILInstance>>
map<ILInstanceKey, ILInstance, less<PropertyName>, allocator<ILInstance>>
iterator
const_iterator
iterator
value_compare
value_compare
iterator
const_iterator
allocator<Property>
iterator
map<PropertyName, Property, less<PropertyName>, allocator<Property>>
list<BaseClass*, allocator<BaseClass*>>
iterator
value_compare
const_iterator
stack<Block*, deque<Block*, allocator<Block*>>>
deque<Block*, allocator<Block*>>
iterator
const_iterator
allocator<Block*>
iterator
const_iterator
iterator
ProjectFile
allocator<Entity*>
value_compare
map<string, SectionContents, less<string>, allocator<SectionContents>>
list<Entity*, allocator<Entity*>>
list<TempResult, allocator<TempResult>>
iterator
const_iterator
iterator
map<void*, Entity*, less<void*>, allocator<Entity*>>
value_compare
allocator<SectionContents>
iterator
const_iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<SectionContents>>
iterator
const_iterator
allocator<TempResult>
allocator<Entity*>
iterator
const_iterator
TempResult
set<STD_Ptr<Cell>, CellLessByElementID, allocator<STD_Ptr<Cell>>>
allocator<STD_Ptr<Cell>>
49
allocator<Element*>
list<Element*, allocator<Element*>>
iterator
const_iterator
allocator<Actual>
list<Actual, allocator<Actual>>
iterator
const_iterator
allocator<Constant*>
list<Constant*, allocator<Constant*>>
iterator
iterator
multiset<TypeRefHack, LessByReferencedType, allocator<TypeRefHack>>
allocator<TypeRefHack>
Figure 40: Bottom part of Himsolt graph A00.
iterator
basic_string<char, char_traits<char>, allocator<char>>
allocator<char>
const_iterator
const_iterator
STD_Ptr<TemplateParameter>
list<STD_Ptr<TemplateParameter>, allocator<STD_Ptr<TemplateParameter>>>
iterator
const_iterator
allocator<STD_Ptr<TemplateParameter>>
CppModelFactory
codecvt<wchar_t, char, mbstate_t>
ModelFactory
multiset<RoutineTypeHack, LessByParamTypes, allocator<RoutineTypeHack>>
num_put<char, _Iter>
allocator<RoutineTypeHack>
_Tree<RoutineTypeHack, value_type, _Kfn, LessByParamTypes, allocator<RoutineTypeHack>>
codecvt<char, char, state_type>
codecvt_base
iterator
const_iterator
numpunct<char>
facet
_Locimp
failure
underflow_error
runtime_error
range_error
vector<_Bool, _Bool_allocator>
reference
overflow_error
bad_cast
reverse_iterator<iterator, value_type, reference, reference*, difference_type>
length_error
iterator
const_iterator
bad_alloc
out_of_range
reverse_iterator<const_iterator, value_type, const_reference, const_reference*, difference_type>
logic_error
exception
invalid_argument
domain_error
bad_exception
iterator
const_iterator
bad_typeid
iterator
__non_rtti_object
value_compare
map<Cell*, Cell*, less<Cell*>, allocator<Cell*>>
list<Cell*, allocator<Cell*>>
allocator<Cell*>
iterator
const_iterator
SectionNotFound
FileNotInProject
FileException
Property
PropertyValue
VariableNotFound
Exception
list<PropertyValue, allocator<PropertyValue>>
iterator
const_iterator
basic_streambuf<char, char_traits<char>>
allocator<PropertyValue>
basic_filebuf<char, char_traits<char>>
locale
basic_ostream<wchar_t, char_traits<wchar_t>>
basic_ios<wchar_t, char_traits<wchar_t>>
ios_base
basic_istream<wchar_t, char_traits<wchar_t>>
basic_fstream<char, char_traits<char>>
basic_ostream<char, char_traits<char>>
basic_iostream<char, char_traits<char>>
basic_streambuf<wchar_t, char_traits<wchar_t>>
basic_istream<char, char_traits<char>>
basic_ios<char, char_traits<char>>
50
51
88
87
86
92
93
91
34
69
57
72
70
65
43
22
67
66
28
61
80
46
39
32
64
25
78
17
12
42
81
31
2
37
71
15
73
9
19
53
4
0
41
59
77
20
62
1
14
5
18
55
60
27
74
26
24
23
85
52
3
10
35
82
38
83
45
13
76
84
16
56
54
11
7
47
63
6
44
95
8
75
30
96
94
33
36
21
97
98
99
68
50
90
49
79
29
58
51
48
40
89
Figure 41: Graph B00-A - circular layout (first prize).
52
92
76
86
80
67
94
72
68
47
81
100
79
61
57
24
32
30
33
39
27
42
22
73
26
63
51
49
82
31
62
25
66
37
71
12
19
9
44
60
97
5
55
77
16
41
91
48
4
40
78
1
50
74
45
85
46
2
0
58
99
34
64
23
90
38
3
6
56
95
43
28
7
53
20
52
36
54
13
15
35
59
29
11
10
14
89
17
18
70
8
75
87
69
21
83
93
96
88
65
84
98
Figure 42: Graph B00-B - circular layout.
3 Green
13 Green
11 Green
1 Green
0 Green
17 Green
9 Green
2 Green
12 Green
81 Green
5 Green
15 Green
14 Green
18 Green
10 Green
16 Green
4 Green
8 Green
7 Green
6 Green
92 Blue
91 Blue
82 Blue
83 Blue
84 Blue
85 Blue
86 Blue
87 Blue
88 Blue
93 Blue
89 Blue
96 Blue
97 Blue
98 Blue
99 Blue
90 Blue
94 Blue
95 Blue
78 Yellow
64 Yellow
25 Yellow
32 Yellow
74 Yellow
26 Yellow
27 Yellow
52 Yellow
55 Yellow
23 Yellow
60 Yellow
62 Yellow
24 Yellow
20 Yellow
77 Yellow
46 Yellow
61 Yellow
80 Yellow
28 Yellow
39 Yellow
34 Yellow
43 Yellow
72 Yellow
22 Yellow
57 Yellow
69 Yellow
70 Yellow
65 Yellow
66 Yellow
67 Yellow
31 Yellow
37 Yellow
42 Yellow
71 Yellow
19 Yellow
41 Yellow
53 Yellow
59 Yellow
73 Yellow
29 Yellow
79 Yellow
40 Yellow
21 Yellow
36 Yellow
48 Yellow
49 Yellow
50 Yellow
51 Yellow
58 Yellow
68 Yellow
44 Yellow
45 Yellow
54 Yellow
75 Yellow
33 Yellow
63 Yellow
56 Yellow
30 Yellow
76 Yellow
47 Yellow
38 Yellow
35 Yellow
53
3 Green
13 Green
11 Green
1 Green
0 Green
17 Green
9 Green
2 Green
12 Green
81 Green
5 Green
15 Green
14 Green
18 Green
10 Green
16 Green
4 Green
8 Green
7 Green
6 Green
92 Blue
91 Blue
82 Blue
83 Blue
84 Blue
85 Blue
86 Blue
87 Blue
88 Blue
93 Blue
89 Blue
96 Blue
97 Blue
98 Blue
99 Blue
90 Blue
94 Blue
95 Blue
78 Yellow
64 Yellow
25 Yellow
32 Yellow
74 Yellow
26 Yellow
27 Yellow
52 Yellow
55 Yellow
23 Yellow
60 Yellow
62 Yellow
24 Yellow
20 Yellow
77 Yellow
46 Yellow
61 Yellow
80 Yellow
28 Yellow
39 Yellow
34 Yellow
43 Yellow
72 Yellow
22 Yellow
57 Yellow
69 Yellow
70 Yellow
65 Yellow
66 Yellow
67 Yellow
31 Yellow
37 Yellow
42 Yellow
71 Yellow
19 Yellow
41 Yellow
53 Yellow
59 Yellow
73 Yellow
29 Yellow
79 Yellow
40 Yellow
21 Yellow
36 Yellow
48 Yellow
49 Yellow
50 Yellow
51 Yellow
58 Yellow
68 Yellow
44 Yellow
45 Yellow
54 Yellow
75 Yellow
33 Yellow
63 Yellow
56 Yellow
30 Yellow
76 Yellow
47 Yellow
38 Yellow
35 Yellow
Figure 43: Matrix representation of graph B00-A.
9 Green
16 Green
17 Green
8 Green
11 Green
13 Green
7 Green
6 Green
2 Green
4 Green
5 Green
19 Green
62 Green
12 Green
18 Green
14 Green
1 Green
0 Green
3 Green
20 Green
15 Green
10 Green
66 Blue
76 Blue
86 Blue
92 Blue
94 Blue
67 Blue
72 Blue
80 Blue
68 Blue
82 Blue
63 Blue
73 Blue
81 Blue
100 Blue
79 Blue
97 Blue
74 Blue
77 Blue
78 Blue
91 Blue
85 Blue
71 Blue
99 Blue
90 Blue
64 Blue
95 Blue
69 Blue
70 Blue
75 Blue
83 Blue
87 Blue
89 Blue
93 Blue
96 Blue
84 Blue
65 Blue
88 Blue
98 Blue
21 Yellow
47 Yellow
33 Yellow
55 Yellow
39 Yellow
30 Yellow
57 Yellow
24 Yellow
32 Yellow
51 Yellow
48 Yellow
26 Yellow
22 Yellow
61 Yellow
49 Yellow
31 Yellow
40 Yellow
56 Yellow
25 Yellow
44 Yellow
60 Yellow
37 Yellow
41 Yellow
23 Yellow
34 Yellow
38 Yellow
45 Yellow
46 Yellow
50 Yellow
58 Yellow
52 Yellow
53 Yellow
43 Yellow
36 Yellow
54 Yellow
28 Yellow
35 Yellow
29 Yellow
59 Yellow
42 Yellow
27 Yellow
54
9 Green
16 Green
17 Green
8 Green
11 Green
13 Green
7 Green
6 Green
2 Green
4 Green
5 Green
19 Green
62 Green
12 Green
18 Green
14 Green
1 Green
0 Green
3 Green
20 Green
15 Green
10 Green
66 Blue
76 Blue
86 Blue
92 Blue
94 Blue
67 Blue
72 Blue
80 Blue
68 Blue
82 Blue
63 Blue
73 Blue
81 Blue
100 Blue
79 Blue
97 Blue
74 Blue
77 Blue
78 Blue
91 Blue
85 Blue
71 Blue
99 Blue
90 Blue
64 Blue
95 Blue
69 Blue
70 Blue
75 Blue
83 Blue
87 Blue
89 Blue
93 Blue
96 Blue
84 Blue
65 Blue
88 Blue
98 Blue
21 Yellow
47 Yellow
33 Yellow
55 Yellow
39 Yellow
30 Yellow
57 Yellow
24 Yellow
32 Yellow
51 Yellow
48 Yellow
26 Yellow
22 Yellow
61 Yellow
49 Yellow
31 Yellow
40 Yellow
56 Yellow
25 Yellow
44 Yellow
60 Yellow
37 Yellow
41 Yellow
23 Yellow
34 Yellow
38 Yellow
45 Yellow
46 Yellow
50 Yellow
58 Yellow
52 Yellow
53 Yellow
43 Yellow
36 Yellow
54 Yellow
28 Yellow
35 Yellow
29 Yellow
59 Yellow
42 Yellow
27 Yellow
Figure 44: Matrix representation of graph B00-B.
9 Green
16 Green
17 Green
8 Green
11 Green
13 Green
7 Green
6 Green
2 Green
4 Green
5 Green
19 Green
62 Green
12 Green
18 Green
14 Green
1 Green
0 Green
3 Green
20 Green
15 Green
10 Green
66 Blue
76 Blue
86 Blue
92 Blue
94 Blue
67 Blue
72 Blue
80 Blue
68 Blue
82 Blue
63 Blue
73 Blue
81 Blue
100 Blue
79 Blue
97 Blue
74 Blue
77 Blue
78 Blue
91 Blue
85 Blue
71 Blue
99 Blue
90 Blue
64 Blue
95 Blue
69 Blue
70 Blue
75 Blue
83 Blue
87 Blue
89 Blue
93 Blue
96 Blue
84 Blue
65 Blue
88 Blue
98 Blue
21 Yellow
47 Yellow
33 Yellow
55 Yellow
39 Yellow
30 Yellow
57 Yellow
24 Yellow
32 Yellow
51 Yellow
48 Yellow
26 Yellow
22 Yellow
61 Yellow
49 Yellow
31 Yellow
40 Yellow
56 Yellow
25 Yellow
44 Yellow
60 Yellow
37 Yellow
41 Yellow
23 Yellow
34 Yellow
38 Yellow
45 Yellow
46 Yellow
50 Yellow
58 Yellow
52 Yellow
53 Yellow
43 Yellow
36 Yellow
54 Yellow
28 Yellow
35 Yellow
29 Yellow
59 Yellow
42 Yellow
27 Yellow
3 Green
13 Green
11 Green
1 Green
0 Green
17 Green
9 Green
2 Green
12 Green
81 Green
5 Green
15 Green
14 Green
18 Green
10 Green
16 Green
4 Green
8 Green
7 Green
6 Green
92 Blue
91 Blue
82 Blue
83 Blue
84 Blue
85 Blue
86 Blue
87 Blue
88 Blue
93 Blue
89 Blue
96 Blue
97 Blue
98 Blue
99 Blue
90 Blue
94 Blue
95 Blue
78 Yellow
64 Yellow
25 Yellow
32 Yellow
74 Yellow
26 Yellow
27 Yellow
52 Yellow
55 Yellow
23 Yellow
60 Yellow
62 Yellow
24 Yellow
20 Yellow
77 Yellow
46 Yellow
61 Yellow
80 Yellow
28 Yellow
39 Yellow
34 Yellow
43 Yellow
72 Yellow
22 Yellow
57 Yellow
69 Yellow
70 Yellow
65 Yellow
66 Yellow
67 Yellow
31 Yellow
37 Yellow
42 Yellow
71 Yellow
19 Yellow
41 Yellow
53 Yellow
59 Yellow
73 Yellow
29 Yellow
79 Yellow
40 Yellow
21 Yellow
36 Yellow
48 Yellow
49 Yellow
50 Yellow
51 Yellow
58 Yellow
68 Yellow
44 Yellow
45 Yellow
54 Yellow
75 Yellow
33 Yellow
63 Yellow
56 Yellow
30 Yellow
76 Yellow
47 Yellow
38 Yellow
35 Yellow
Figure 45: Matrix representation of non empty part of graphs B00-A and B00-B.
55
3 Green
13 Green
11 Green
1 Green
0 Green
17 Green
9 Green
2 Green
12 Green
81 Green
5 Green
15 Green
14 Green
18 Green
10 Green
16 Green
4 Green
8 Green
7 Green
6 Green
92 Blue
91 Blue
82 Blue
83 Blue
84 Blue
85 Blue
86 Blue
87 Blue
88 Blue
93 Blue
89 Blue
96 Blue
97 Blue
98 Blue
99 Blue
90 Blue
94 Blue
95 Blue
78 Yellow
64 Yellow
9 Green
25
Yellow
16Yellow
Green
32
17Yellow
Green
74
8
26 Green
Yellow
11
Green
27 Yellow
13
Green
52 Yellow
7 Green
55
Yellow
6
Green
23 Yellow
2 Yellow
Green
60
4 Yellow
Green
62
5 Yellow
Green
24
19Yellow
Green
20
62Yellow
Green
77
12Yellow
Green
46
18Yellow
Green
61
14Yellow
Green
80
1
Green
28 Yellow
0
Green
39 Yellow
3
Green
34 Yellow
20Yellow
Green
43
15Yellow
Green
72
10Yellow
Green
22
66Yellow
Blue
57
76Yellow
Blue
69
86Yellow
Blue
70
92Yellow
Blue
65
94Yellow
Blue
66
67Yellow
Blue
67
72
Blue
31 Yellow
80
Blue
37 Yellow
68
Blue
42 Yellow
82
Blue
71 Yellow
63
Blue
19 Yellow
73Yellow
Blue
41
81Yellow
Blue
53
100Yellow
Blue
59
79Yellow
Blue
73
97Yellow
Blue
29
74Yellow
Blue
79
77Yellow
Blue
40
78Yellow
Blue
21
91Yellow
Blue
36
85
Blue
48 Yellow
71
Blue
49 Yellow
99
Blue
50 Yellow
90Yellow
Blue
51
64Yellow
Blue
58
95Yellow
Blue
68
69Yellow
Blue
44
70Yellow
Blue
45
75Yellow
Blue
54
83Yellow
Blue
75
87Yellow
Blue
33
89
Blue
63 Yellow
93
Blue
56 Yellow
96
Blue
30 Yellow
84
Blue
76 Yellow
65
Blue
47 Yellow
88Yellow
Blue
38
98Yellow
Blue
35
21 Yellow
47 Yellow
33 Yellow
55 Yellow
39 Yellow
30 Yellow
57 Yellow
24 Yellow
32 Yellow
56
In 2001 Graph Drawing Conference was helt in Vienna and the contest was organised by
Franz Brandenburg. Rules and data are described at:
http://www.ads.tuwien.ac.at/gd2001/
Graph A01
¶ÂÁÃ¶
In a given set of units
¶
Ä
Ä
(articles, books, works, . . . ) we introduce a
¹ºT»bºT¼k½
relation
¾À¿
Ä
¾ÆÅÇÈÅ cites
Ä
Ä
Ä
Ä isÄ usually irreflexive, Ê
É
¢
¶
¤ ¾ ¦ . A citing relation
which determines a citation network
¶Ë´Ì ¾ , and (almost) acyclic, Ê @¶ ÊÍ IN ´Ì ¾8Î . The citation network is
standardized by adding, if necessary, artificial source vertex and sink or terminal vertex »
¢¤ ¦
and the arc » (see figure).
An approach to the analysis of citation network is to determine for each unit / arc its
importance or weight. These values are used afterwards to determine the essential substructures in the network. Hummon and Doreian (1989, 1990) [1, 2, 3] proposed three methods
of assigning weights
IR to arcs:
Ï ´ ¾@Ð
Ñ
57
Ï ¢ £Ò¤N¥¦ © ¾ÔÓ ¢ £¦ ©1ÕH© ¾ ¢ ¥§¦ ©
¡3¢ £Ò¤N¥¦Ö ª ¢ £Ò¤N¥§¦ , where ª ¢ £Ò¤N¥¦ denotes the number of
Paths count method: Ï
¢ £Ò¤N¥¦
different paths from ×³ØoÙ¾ to ×³Ú1ÛÜ¾ (or from to » ) through the arc
¢ £ ¤N¥§¦ß ªÖà ¢ £Ò¤N¥§¦ , where ªÖà ¢ £Ò¤N¥§¦ equals to ª ¢ £Ò¤N¥¦ from paths
SPLC method: ÏÞÝ
¢É¶¤ ¾ à ¦ , ¾ à ´¢ ¾ ¬á± ·1¦âÁ¢É¶äãK± ¤ » ·1¦
count method over the network
The last two methods are efficiently (Batagelj, 1991, 1994) [4] implemented in Pajek
¢ ¥¦ denotes the number
and can be applied also on (very) large acyclic networks. Let ª Ó
¥
¢ ¥§¦ denotes the number of different paths from ¥ to
of different paths from to , and ª
¢
Ò
£
N
¤
¥
u
¦
¢
£
¦
¢
¥
:
¦
¤
¢ £Ò¤N¥§¦Ü ¾ .
ª Ó Õª
» . Then ª
ª and ªÖà are flows in the network since they obey the Kirchoff’s node law:
¥
¢É¶¤ ¾ ¦ in standard form it holds
For every node in a citation network
incoming flow outgoing flow
¢¤ ¦
Therefore the total flow through the citation network equals ª » . This gives us a natural
way to normalize the weights
¢Ï £Ò¤N¥¦u ª ¢ ¢ £Ò¤ ¤N¥¦ ¦ å æç Ï ¢ £ ¤N¥§¦ ç²è
ª » If é is a minimal cut-set it also holds ê
¢ £Ò¤N¥¦ è
Ï
ëì-í î:ïZðñ
NPCC method:
We can assign weights also to vertices
¢Ï ¥¦uáª Ó ¢ ¥§¦ ¢ Õ ¤ ª ¦ ¢ ¥§¦
ª » References
Layouts of graph A
In graph A the relation is the reverse of the citing relation. The original graph A has 311
vertices. It has 6 weak components. Searching for strong components (testing acyclicity)
it turns out that the graph A is not acyclic. A large strong component was generated by
an erroneous arc ( GD94/143 Eades, GD98/423 Eades). After reversing it 4 small strong
components remained, corresponding to mutual references GD94/286 Garg, GD94/298
Papakostas , GD94/328 Di Battista, GD94/340 Bose, GD94/352 ElGindy , GD95/8
Alt, GD95/234 Fekete and GD95/140 Chandramouli, GD95/300 Heath . To obtain
an acyclic graph, required by citations analysis method, we applied the following ’preprint’
transformation:
· ±
·
±
±
·
· ±
58
Each paper from a strong component is duplicated with its ’preprint’ version. The papers
inside strong component cite preprints.
The pictures were exported as nested partitions into SVG format that allows interactive
display of different slices – subgraphs induced by arcs with weights larger than a threshold
value. These pictures are available at
http://vlado.fmf.uni-lj.si/pub/GD/GD01.htm.
In the paper form we can present only some snapshots.
The first picture displays complete network after ’preprint’ transformations (320 vertices). The vertices are put in layers (vertical position and color of vertices) according to
the years of publication. The placement of vertices inside the layer was determined by local optimization. The width and the color density of an arc and the size of a vertex are
proportional to their citation weights.
The second and the third picture display the main parts (slices) of the citation network
at threshold values 0.02 and 0.05. The red arcs belong to the ’main path’.
59
Figure 46: Graph A – complete graph.
60
Figure 47: Graph A – level 0.02.
61
Figure 48: Graph A – level 0.05.
62
Graph B
To obtain the ’central symmetric’ picture of graph B energy drawing was used, followed
by manual grid positioning of vertices. To save the space the lower part of the picture was
manually mirrored across the vertical axis.
T8-
T0+
T9+
+90 pos
P+90
T8+
turn right
turn left
T8+
T9-
T9+
+22 - +90 intermediate
P-22
T9+
turn right equalizer
+22 pos
T9+
0 - +22 intermediate
T8-
T9+
0 pos
T8+
P+22
P0
T9-
T8+
turn left equalizer
T9-
P0
0 - -22 intermediate
T8T8+
T8+
turn left equalizer
P-22
-22 pos
T8+
-60 pos
T9+
T8+
P-90
T9+
turn right
turn left
P-60
-90 pos
T8+
T9+
T9+
T8-
P-22
T9+
-22 - -90 intermediate
T9-
Figure 49: Graph B – ’central symmetric’.
Graph C
Graph C is an acyclic directed graph. Such graphs can be topologically sorted. The corresponding adjacency matrix has zero lower triangle and diagonal. Since the graph is rather
dense we decided to use the matrix representation to visualize the graph structure. Layers
are represented by blocks divided by blue lines.
63
T8-
turn left
T8+
T0+
T9-
T9+
+22 - +90 intermediate
P+90
P-22
+90 pos
T8+
T9+
turn right
T9+
+22 pos
T9+
P0
0 - +22 intermediate
T8-
P+22
T9-
T8+
T8+
turn left equalizer
0 pos
T9+
0 - -22 intermediate
T8T8+
P-22
turn left equalizer
T8+
-22 pos
T9+
P-90
P-60
T8+
T8+
-90 pos
-22 - -90 intermediate
-60 pos
T9+
T8+
turn left
T8-
T9-
P-22
P0
T9+
T9+
T9+
T9-
Figure 50: Graph B – mirror.
turn right
64
Pajek - shadow [0.00,1.00]
RGC
LGN
V1
V2
V3
VP
PIP
V3A
MDP
MIP
PO
MT
V4t
V4
VOT
VIP
LIP
MST
FST
PIT
7a
FEF
STPp
CIT
46
STPa
AIT
OFC
36
TF
TH
ER
HC
RGC
LGN
V1
V2
V3
VP
PIP
V3A
MDP
MIP
PO
MT
V4t
V4
VOT
VIP
LIP
MST
FST
PIT
7a
FEF
STPp
CIT
46
STPa
AIT
OFC
36
TF
TH
ER
HC
Figure 51: Graph C – matrix representation.
REFERENCES
65
References
[1] Hummon N.P., Doreian P. (1989): Connectivity in a Citation Network: The Development of DNA Theory. Social Networks, 11 39-63.
[2] Hummon N.P., Doreian P. (1990): Computational Methods for Social Network Analysis. Social Networks, 12 273-288.
[3] Hummon N.P., Doreian P., Freeman L.C. (1990): Analyzing the Structure of the
Centrality-Productivity Literature Created Between 1948 and 1979. Knowledge: Creation, Diffusion, Utilization, 11(4), 459-480.
[4] Batagelj V. (1991): An Efficient Algorithm for Citation Networks Analysis. Presented
at EASST’94, Budapest, Hungary, August 28-31, 1994. First presented at the Seminar
on social networks. University of Pittsburgh, January 1991.
[5] Batagelj V., Doreian P., and Ferligoj A. (1992): An Optimizational Approach to Regular Equivalence. Social Networks 14, 121-135.
[6] Brandenburg, F. J. (1996): Graph Drawing. Proceedings of Symposium on Graph
Drawing, GD95, Passau, Germany, September 1995, Springer-Verlag, Lecture Notes
in Computer Science, vol. 1027, 224-233.
[7] DiBattista, G. (1998): Graph Drawing. Proceedings of Symposium on Graph Drawing, GD97, Rome, Italy, September 1997, Springer-Verlag, Lecture Notes in Computer
Science, vol. 1353, 438-445.
[8] Kratochvil, J. (1999): Graph Drawing. Proceedings of Symposium on Graph Drawing, GD99, Stirin Castle, Czeck Republic. September 15-19, 1999. Springer-Verlag,
Lecture Notes in Computer Science, vol. 1731, 400-409.
[9] Marks, J. (2001): Graph Drawing. Proceedings of the 8th Symposium on Graph Drawing, GD00, Colonial Williamsburg, USA. September 20-23, 2000. Springer-Verlag,
Lecture Notes in Computer Science, vol. 1984, 410-418.
[10] North, S. (1997): Graph Drawing. Proceedings of Symposium on Graph Drawing,
GD96, Berkeley, California, USA, September 1996, Springer-Verlag, Lecture Notes
in Computer Science, vol. 1190, 129-138.

Our submissions for GD contests 1995-01

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