Upload
others
View
7
Download
0
Embed Size (px)
Citation preview
UNIVERSITY OF LJUBLJANA
INSTITUTE OF MATHEMATICS, PHYSICS AND MECHANICS
DEPARTMENT OF THEORETICAL COMPUTER SCIENCE
JADRANSKA 19, 1 000 LJUBLJANA, SLOVENIA
Preprint series, Vol. 40 (2002), 568/2
LAYOUTS FORGRAPH DRAWING CONTESTS
1995-2001
Vladimir Batagelj, Andrej Mrvar
ISSN 1318-4865
Version 1: May 13, 1998Version 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, Departmentof Mathematics, and IMFM Ljubljana, Department of TCS, Jadranskaulica 19, 1 000 Ljubljana, Slovenia
e-mail: [email protected]
Ljubljana, December 27, 2001
Layouts forGraph Drawing Contests
1995-2001
Vladimir BatageljDepartment of Mathematics, University of Ljubljana
Andrej MrvarFaculty of Social Sciences, University of Ljubljana
Graph drawing contests
Since 1994 graph drawing contests are organized as a part of the Graph Drawing Confer-ences. The rules and data are described on Internet and participants send their drawingstill the specified date. They can use any technique to get layouts of graphs. The primaryjudging criterion is how well the drawings convey the information in the graphs: vertexidentifiers, vertex types, and vertex interconnectivity. A secondary criterion is the degreeto 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 ingraph-drawing technology.
Data (vertices and lines) for 3 or 4 graphs are given each year. A winning entry for eachgraph is chosen by a panel of experts.
In this paper we collected our submissions to the contests in the years 1995–2001. Theyare available also at
http://vlado.fmf.uni-lj.si/pub/gd/gd95.htmand the original data (and their versions in Pajek format) at
http://vlado.fmf.uni-lj.si/pub/networks/data/gd/gd.htmThere you will find also a longer version of this collection (some pictures are to large forthe format of the preprint publication) and pictures in some (dynamical) graphical formats(VRML, SVG) that can not be adequately reproduced in the paper form.
2
Layouts for Graph Drawing Contest 1995
In 1995 the Graph Drawing Conference was helt in Passau and the contest was organizedby 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 ver-tices on the rectangular net so that the number of crossings of lines is as low aspossible).
� Manual editing was performed to reposition vertices using our graph picture editorDRAW.
Graph B95� Analysing graph B using our program RELCALC two central vertices were found (1and 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 thatthe total length of the lines was minimized.
� Layout was then edited manually using DRAW to reposition vertices to minimizecrossings (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 ofENERGy).
� 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.htmThe complete report of the contest is available in [6] and:
http://www.merl.com/reports/TR95-14/index.html
3
1
2
3
4
5 6
78
9
10
11
12
13
1415
16
17
18
19
20
21
222324
25
26
27
28
29
30
31
32
33
34
35
36
Figure 1: Graph A95.
4
1
2
3
4
5
6
7 89
10
11
12
13
14
15
16
17 18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
3435
36
37
38
39
40
41
42
43
44
45 46
47
48
49
50
51
52
53
54
5556 57 58
59
60
6162
63
64
65
66
67
68
69
70
71
7273
Figure 2: Graph B95 (honorable mention).
5
1
2
3
4
5
6
7
8
9
10
11
1213
14
15
16
17
18
1920
21
22
23
24
25
26
2728
29
30
3132
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
5152
53
54
55
56
57
58
59
60
61
62
Figure 3: Graph C95 (first prize).
6
Layouts for Graph Drawing Contest 1996
In 1996 Graph Drawing Conference was helt in Berkeley, and the contest was organized byPeter 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 ver-tices on the rectangular net so that the number of crossings of lines is as low aspossible).
� Manual editing was performed to reposition vertices using our graph picture editorDRAW.
The layout was awarded the honorable mention.
Graph C96� Analysing graph C using our program RELCALC two parts and 2 connecting verticeswere found.
� Each part was handled separately using our program ENERG (minimisation of en-ergy). One part consists of a lattice structure, and the second of a planar graph ofcylindric symmetries. This spatial picture was realized in VRML (produced from thedescription in our graph description language NetML based on SGML).� Some manual editing was done for planar representation.
The layout was awarded the first prize.
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 DRAWwas performed to reposition vertices to avoid cross-ings.
7
1
2
34
5
6
7
8
9
10
11
1213
14
15
16
17
18
19
20 21
22
23
24
25
26
27
28
29
3031
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
5556
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
8384
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101102
103
104
105
106
107
108
109
110
111
Figure 4: Graph B96 (honorable mention).
See: http://vlado.fmf.uni-lj.si/pub/gd/gd96.htmThe complete report of the contest is available in [10] and:
http://www.merl.com/reports/TR96-24/index.html
8
1
23
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
30
31
32
33
34
35
36
37
3839
40
41
42
43
44
45
46
47
48
49
50
5152
53
54
55
56
57
58
59
60
61
62
63
64
0
Figure
5:G
raphC
96(firstprize).
9
Figure 6: Graph C96 / VRML snapshot.
10
Figure 7: Graph C96 with cylinder / VRML snapshot.
11
1
2
3
4
5 6
7
8
9 10
11
12
13
14
15
16
1718
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
5253
54
55
5657
58
5960
61
62
63
64
65
66
67
68 69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
9091
92
93 94
9596 97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113114
115116
117
118119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142143
144
145
146
147
148
149
150
151
152
153
154155
156
157
158
159
160
161
162
163
164
165 166
167
168169
170
171
172173
174
175
176
177
178
179
180
Figure 8: Graph D96.
12
Layouts for Graph Drawing Contest 1997
In 1997 Graph Drawing Conference was helt in Rome and the contest was organised byPeter 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 pro-gram Pajek. Manual editing was used to reposition vertices in the grid to obtainorthogonal layout in plane.
The layout was awarded the first prize.
� Manual editing in 3D was performed to get orthogonal embeddings in space: mini-mal, symmetric and cube.
Graph B97� Analysing graph B using our program MODEL we obtained (almost) regular partitionin 3 classes. The third class contains only vertex Harmony Central. The secondclass, represented by squares, contains 11 vertices that are connected only to thevertices in the class 1 (represented by circles). Vertices in class 1 are also connectedto other vertices in the same class. We first drew all vertices in the class 1 in the centerand vertices in class 2 separately – using class shrinking and circular drawing optionsin Pajek. Afterward we manually moved vertices of class 1 connected to only onevertex of class 2 close to this vertex. Finally we manually arranged the remainingvertices of class 1.
� We transformed given similarities � on arcs to dissimilarities��� ����� and applied
Ward’s hierarchical clustering method to the obtained dissimilarity matrix. We pro-duced a clustering into 12 clusters, shrank the graph using Pajek, and draw the ob-tained skeleton minimizing the number of crossings. Finally we manually arrangedthe vertices of original graph.
The layout was awarded the first prize.
See alsohttp://vlado.fmf.uni-lj.si/pub/gd/gd97.htm
The complete report is available in [7] or athttp://www.merl.com/reports/TR97-16/index.html
13
1
2
3
4
5
6
78
910
11
12
13
14
15
16
17
18
19
20
21
22
23
2425
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45 46
47
48
49
50
51
52
53 54
55
56
5758
59
60
61
62
63
64
65
66
67
68 69
7071
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109 110
111 112
113
114
115
116
117 118
119 120
Figure 9: Graph A97 – orthogonal layout in plane (first prize).
14
Figure 10: Graph A97 – 3D minimal / VRML snapshot.
15
Figure 11: Graph A97 – 3D symmetric / VRML snapshot.
16
Figure 12: Graph A97 – 3D cube / VRML snapshot.
17
1997 North American Gs Develop
Edirol Online
Virtual Sound Canvas Online
Microsoft Corporation Home Pag
Microsoft Netshow Events Calen
Wavelet Netcare
Wavelab
Wavelet Resources
IBM Corporation
Kasparov Vs. DeepBlue: The Rem
Guest Essay: David Stork
Boston At Night: Feature Story
Intranet Executive: Digital Id
Netscape Navigator Family
Netscape Devedge: Library
Netscape Devedge: Library 1
Netscape Devedge: Courses & Co
Netscape Devedge: Courses & Co
Four Corners Hantavirus
Bunyaviridae
INI International: Grocery Sec
INI International: Vitamins
INI International: Candy Secti
Journal EntryCelery
Onions
The Biting Truth
Musky Have Teeth
404 Not Found
Cold Front Tactics
Identifying Vegetation
Tackle Box Survival - Surface
Sandell & Associates Surface L
Musky Muskie Lure Components
Young Designer Of The Month
The London College Of Fashion
Designercity
Designercity1
Designercity2
Designercity3
Designercity4
Designercity5
Designercity6
Nada138-954
Janet’s Horsin’ Around On The
Equinet(tm) - Comments
Harmony Central: Midi Tools
Figure 13: Graph B97 – regular equivalence.
18
��� ������������������ �!� "$#%�!&'�)( �+*-,+./&).10324245687:9-;'<>=@?�6BADCFEHGIKJ�LNMPO J:Q RIKJ�LNMPO MTSTU$MTV WIKJ�LNMPO MTSTXYMZS [\Y]_^a`bJ�L_c dec f gNhikjHMTVTc lm^bMNdon pNq\3c SZc ^blsr3dt]bS gNRnu]�VavZ`Pr$MaMTSZw gNW\1xPVySzxm^N{|X)c S }ag~ ^_^bMTSTj|c l�~ f }ap� x�O f���d�x�^bSzr pNhXYJPf:J�}apsWN�sqb� �N�����]_c ^bMTS�rkn �_[� � x_dt^PMPd�V���L }a�� � n�c fmc r$x:xmO �_R� MNO MNd ` gNq� ^_c xm^�V gN[�bx�]_d!^PJ:O ��^bS gb�~ fN�HMTlsMTSyJbSZ^ p�}r1JP�PvNO Ms\1xa�N� pNg��J:^bf_MNO O ���HV pNp~�X�~ �)dFx:�aMPd�` g�}~�X�~ �'c SyJ:�+c ^ gNg~�X�~ � J:^bfs`N��� gNp�4c d��mx�]:^bf �-� pj)J�L:c f���Szx_dtv }N}�3JbVa�PJNd�xPLmj4\ }ahn%�1X3MTSoVawPxT� � q�:�3x_d�VTc ^_� �|d �_q�Pxm^bf:x�^:�sJ�Vaw pN[}a�s�NRmX3�'�+�-V�j }��fmc d�xmO � ^�� gn%�1�3xm��MN��JblsM �~�\Hn � xsdt�_xsd�J �XY��XYJ�L_c l:J�SZd }Z�nu]�VavZ`mn��:]_dFM pb�XY��jHMZL � x_� � x�}aW�_hP��X3ST�Pxm]_^Pf gN�XY��jHMZL��:c QNd ` }aqXY��jHMZL��:c QNd!} }a[XY��jHMZL � x_� � x�}aRjHMTVTc lm^P�Pc S q �_gjHMTVTc lm^P�Pc S [ �_pjHMTVTc lm^P�Pc S g pN�jHMTVTc lm^P�Pc Sa} pNWjHMTVTc lm^P�Pc Se` pNRjHMTVTc lm^P�Pc Sz� ��}jHMTVTc lm^P�Pc S p �_h
Figure 14: Graph B97 – Dendrogram for Ward’s method.
19
1997 North American Gs Develop
Edirol Online
Virtual Sound Canvas
Microsoft Corporation Home Pag
Microsoft Netshow Events Calen
Wavelet NetcareWavelab
Wavelet Resources
IBM Corporation
Kasparov Vs. DeepBlueGuest Essay: D. Stork
Boston At Night: Feature StoryIntranet Executive: Digital Id
Netscape Navigator Family
Netscape Devedge: Library
Netscape Devedge: Library 1Netscape Devedge: Courses & Co
Netscape Devedge: Courses & Co
Four Corners Hantavirus
Bunyaviridae
INI International: Grocery Sec
INI International: VitaminsINI International: Candy Secti
Journal EntryCeleryOnions
The Biting Truth
Musky Have Teeth
404 Not Found
Cold Front Tactics
Identifying Vegetation
Tackle Box Survival - Surface Sandell & Associates Surface L
Musky Muskie Lure Components
Young Designer Of The Month
The London College Of Fashion
Designercity
Designercity1Designercity2
Designercity3Designercity4
Designercity5Designercity6
Nada138-954
Janet’s Horsin’ Around On The
Equinet(tm) - Comments
Harmony Central: Midi Tools
Figure 15: Graph B97 – Ward’s clustering (first prize).
20
Layouts for Graph Drawing Contest 1998
In 1998 Graph Drawing Conference was helt in Montreal and the contest was organised byPeter 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 graphchanges over time. In our solution addition and deletion operations were performed usingmacro language which is recognized by program package Pajek. Then we used Mi-crosoft Camcorder (free software) to record the process. Selected layouts in threedifferent time points are shown.
Graph B98
Symmetries in graph (with some exceptions) can easily be noticed. We started the draw-ing using the layout obtained using Fruchterman-Reingold spring embedder. Later we usedmanual editing to maximize symmetries and made some displacements according to differ-ent sizes and shapes of nodes. Pajek was used to do all the work.
The layout was awarded the first prize.
Graph C98
Using spring embedders we could not get any nice layouts. Analysing graph we found thatit is a symmetric cubic graph. Later we used eigenvectors approach and computed eigenvec-tors 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 (equiva-lences) some of the nodes are drawn on the same positions and some are overlapping whenselecting the certain view to see the symmetries. Since some vertices are overlapping webuilt 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 thatis inspired or related to graph drawing. We decided to generate graph from dictionary andsent some interesting subgraph of it.
21
Table 1: Overlapping vertices in graph C98
Group Color Vertices1. Yellow 13, 762. Green 9, 12, 33,1063. Pink 39, 65, 88,1124. Blue 5, 20, 51, 635. Fuchsia 68, 75, 85, 926. White 36, 997. Orange 21, 428. Purple 23, 24, 55, 899. NavyBlue 30, 44, 54, 57
10. TealBlue 3, 11, 43,10111. OliveGreen 1, 18, 64, 74, 91,103,104,10712. Gray 19, 26, 47, 5913. Black 17, 40, 70, 7914. Maroon 48, 5315. LightGreen 25, 32, 35, 60, 66, 71, 73,10516. Cyan 10,10217. Yellow 2, 22, 81, 9018. Green 14, 58, 61, 8319. Pink 4, 15, 46, 52, 77, 78,109,11020. Blue 7, 8, 27, 4121. Fuchsia 6, 50, 67, 9622. White 82, 84, 95, 9723. Orange 31, 8024. Purple 16, 29, 98,10825. NavyBlue 38, 72, 86, 8726. TealBlue 37, 4527. OliveGreen 28, 62, 93,11128. Gray 34, 49, 56,10029. Black 69, 94
Large graph can be generated from words in a dictionary. We constructed a graph inwhich two words are connected iff one can be obtained from the other by changing sin-gle 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 shortestpaths between graph and drawing and between drawing and contest, draw the ob-tained graph using layers option in Pajek (layers are determined by distance from draw-ing). Additionally we added two puzzles:� one difficult: find shortest paths alone,
22
Figure 16: Graph C98.
� one easy: find only missing words on the paths.
See also: http://vlado.fmf.uni-lj.si/pub/gd/gd98.htm
23
www.att.com/catalog/consumer
www.att.com
www.att.com/att
www.att.com/cmd/custcare
www.att.com/write
www.att.com/worldnet
www.att.com/terms.html
www.att.com/learningnetwork
www.att.com/cgi-bin/ppps.cgi
www.att.com/catalog/small_businesswww.att.com/whatsnew
www.att.com/cgi-bin/bmd_cart.cgi
www.att.com/cmd/jump
www.att.com/catalog
www.att.com/textindex.html
www.att.com/bmd/tollfree
www.att.com/worldnet/wmis
search.att.com
www.att.com/bmd/jump
www.att.com/features
www.att.com/rock
www.att.com/home
Figure
17:G
raphA
98,afterexecuting
deletion:deletewww.att.com->www.att.com/catalog/consumer
(23operations
executed).
24
www.att.com/catalog/consumer
www.att.com
www.att.com/att
www.att.com/write
www.att.com/worldnet
www.att.com/terms.html
www.att.com/cgi-bin/ppps.cgi
www.att.com/catalog/small_businesswww.att.com/whatsnew
www.att.com/cgi-bin/bmd_cart.cgi
www.att.com/cmd/jump
www.att.com/catalog
www.att.com/textindex.html
www.att.com/worldnet/wmis
search.att.com
www.att.com/bmd/jump
www.att.com/features
www.att.com/rock
www.att.com/home
www.att.com/services
www.att.com/net
www.att.com/worldnet/wis/sky/signup.html
www.att.com/bmd/products
www.att.com/news
www.att.com/worldnet/intranet
Figure
18:G
raphA
98,afterexecuting
deletion:deletewww.att.com/whatsnew->www.att.com/catalog/consumer
(38operations
executed).
25
www.att.com/catalog/consumer
www.att.com
www.att.com/att
www.att.com/cmd/custcare
www.att.com/write
www.att.com/worldnet
www.att.com/terms.html
www.att.com/learningnetwork
www.att.com/cgi-bin/ppps.cgi
www.att.com/catalog/small_businesswww.att.com/whatsnew
www.att.com/cgi-bin/bmd_cart.cgi
www.att.com/cmd/jump
www.att.com/catalog
www.att.com/textindex.html
www.att.com/bmd/tollfree
www.att.com/worldnet/wmis
search.att.com
www.att.com/bmd/jump
www.att.com/features
www.att.com/rock
www.att.com/home
www.att.com/services
www.att.com/net
www.att.com/worldnet/wis/sky/signup.html
www.att.com/bmd/products
www.att.com/news
www.att.com/worldnet/intranet
www.att.com/bmd/custcare
www.att.com/cgi-bin/cart.cgi
www.att.com/cmd
www.att.com/cmd/products
www.att.com/speeches
www.att.com/speeches/index96.html
www.att.com/international
www.att.co.uk
www.att.com/business
www.catalog.att.com/cmd/jump
Figure
19:G
raphA
98,afteralladditions/deletions
done(65
operationsexecuted).
26
1
2 3
4
5
6
7
89
10
11
12
13
14F
152
1
1
1
1
1
2
1
1
1
1
1
12
3 11
2A
2A
3H
1A
3H
2
1
1A
2A 4H
1A
4H
3
0
Tag 1
Tag 2 Tag 3
Tag 4
Tag 5
Tag 6
Tag 7
Tag 8
Tag 9
Tag 10
Tag 11
Tag 12
Tag 13
Tag 14
Tag 15
Tag 16
Tag 17
Tag 18
Tag 19
Tag 20
Tag 21
Tag 22
Tag 23
Tag 24
Tag 25
Tag 26
Tag 27
Tag 28
Tag 29
Tag 30
Tag 31
Tag 32
Tag 33
Tag 34Tag 35
Tag 36
Tag 37Tag 38
Tag 39
Tag 40 Tag 41
Tag 42
Tag 43
Tag 44
Tag 45
Tag 46Tag 47
Tag 48
Tag 49
Tag 50 Tag 51
Tag 52
Tag 53
Tag 54
Tag 55
Tag 56
Tag 57
Tag 58
Tag 59
Tag 60
Tag 61 Tag 62
Tag 63
Tag 64Tag 65
Tag 66
Tag 67
Tag 68
Tag 69Tag 70
Tag 71
Tag 72
Tag 73
Tag 74
Tag 75
Figure
20:G
raphB
98(firstprize).
27
graph
drawing
contestPajek
Figure
21:G
raphD
98:D
ifficultpuzzle.
28
graph
pine
ping
pipe
rape
ripe
aping
grape
grate gripegrapes
graphs
grates
gratin
gratis
raping
rating
craping
crating
draping
grating
drawing
cone
cong
cove
pong
covercovet
covert
content
convent
convert
contestPajek
Figure
22:G
raphD
98:S
olution.
29
Layouts for Graph Drawing Contest 1999
In 1999 Graph Drawing Conference was helt in Stirin (Czeck Republic) and the contestwas organised by Franz Brandenburg, Michael Juenger, Joe Marks, Petra Mutzel, and FalkSchreiber. 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 overtime. 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)
30
– =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 obtainedby Kamada-Kawai spring embedder. Later we used manual editing to arrange them onrectangular net.
Development of the graph over time We used the Pajek option for drawing graphsin different time points. Only time points where at least one vertex or one line changesaccording to last layout were drawn (e.g. 1, 2, 4, 5,...). After each change time the layout ofthe new graph was optimized starting with the previous positions.
The layout was awarded the first prize.
Graph B99
We used eigenvectors approach and computed eigenvectors of Laplacean matrix that corre-spond to the 1st, 2nd and 5th largest eigenvalue. No additional manual editing was used onthe obtained spatial picture. Suitable view was selected to get planar EPS picture. Picturewas 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 embed-der. Later we used manual editing to maximize ’rectangularity’ and made some displace-ments 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].
31
Rosi Koch
Zorro Franz Josef Pichelsteiner
Onkel Franz Franz Wittich
Gung Pahm Kien
Urzula Wienicki
Gabi Zenker-geb.Skawowski
Phil Seegers
Hans Wilhelm Huelsch
Hajo Scholz
Olli Klatt
Erich-Schiller
Helga Beimer Schiller
Hans Beimer Anna Ziegler
Andy Zenker
Berta Griese
Lisa Hoffmeister
Marion Beimer
Klaus Beimer
Dr. Eva-Maria Sperling
Boris Ecker
Valerie Ecker
Iffi Zenker
Momo Sperling
Dr. Ahmet Dagdelen
Else Kling
Paolo Varese
Dani Schmitz
Philipp Sperling
Tanja Schildknecht-Dressler
Dr. Ludwig Dressler
Mary KlingOlaf Kling
Fausto Rossini
Frank DresslerElena Sarikakis
Isolde Pavarotti
Kaethe Georg Eschweiler
Carsten Floeter Theo Klages
Beate Sarikakis
Vasily Sarikakis
Rolf Sattler Bolle Guenther Bollmann
Hilmar Eggers
Wilhelm Loesch
Marlene Schmitt
Friedemann Traube
Wanda Winicki
Pat Wolffson
Winifred Snyder
Irina Winicki
Sophie ZieglerTom Ziegler
Sarah Ziegler
Paula Madalena Francesca Winicki
Canan Dagdelen
Herr Panowski
Giovanna Varese
Marcella Varese
Nico Zenker
Gina Varese
Chromo Hoyonda
Alfredo
Francesco
Professor Dr. Rudolf Tenge-Wegemmann
Frau Horowitz
Harry
Zeki Kurtalan
Fritjof Lothar Boedefeld
Gundel Koch
Dr. Otto Pichelsteiner
Leo Klamm
Rita Bassermann
Simone Fitz
Dora Wittich
Martha
Bruno Skabowski
Sue
Theresa Zenker
Inge Kling
Ernst+Lisl Wiesenhuber
gesch.Skabowski*19.10.1927
*09.08.1963
*24.07.1913
*23.10.1958
*10.02.1963
verw.Zimmermann*23.05.1960
*14.04.1961
*29.02.1952
*09.06.1944
*06.01.1976
*23.07.1944
geb.Wittich*24.03.1940
*03.10.1943 geb.Jenner*14.07.1959
*03.07.1947
geb.Nolte*25.06.1941
*19.10.1981
*21.05.1969
*17.10.1078
*06.08.1947
*17.06.1965
geb.Zenker*08.10.1975
*19.08.1978
*01.04.1975
*14.05.1922
*14.09.1977
geb.Schildknecht*19.06.1970
*27.06.1933
geb.Dankor*30.01.1969*10.11.1955
*31.10.1966*08.11.1939
verw.Panowak*27.11.1936
*05.03.1966
geb.Floeter*17.08.1970
*14.02.1963
*02.07.1942
geb.Kollin*17.07.1938
*05.05.1972
*18.10.1990
*25.07.1991*27.07.1989
*22.10.1987
*29.08.1996
*12.05.1994*25.10.1970
*06.04.1940
*22.05.1962
+1964
Unbekannter_Russe
+1986
*1947+1964
*1955+1965
*19.09.1996
*10.05.1968+29.08.1991
*30.01.1992
*14.11.1991
*1969+1986
*19.04.1996
*13.03.1994
*18.07.1996
*24.07.1997
*26.11.1987+18.08.1996Figure
23:G
raphA
99,currentsituation.
32
Lydia Nolte
Gung Pahm Kien
Gabi Zenker-geb.Skawowski
Helga Beimer Schiller
Hans Beimer
Berta Griese
Marion Beimer
Benny BeimerKlaus Beimer
Franz Schildknecht
Henny Schildknecht
Stefan Nossek
Egon Kling
Else Kling
Tanja Schildknecht-DresslerDr. Ludwig Dressler
Vasily Sarikakis
Chris Barnsteg
Elfie Kronmayr
Sigi Kronmayr
Philo Bennarsch
Joschi Bennarsch
Paul Nolte
Theo Nolte
Lydia Nolte
Gung Pahm Kien
Gabi Zenker-geb.Skawowski
Helga Beimer Schiller
Hans Beimer
Berta Griese
Marion Beimer
Benny BeimerKlaus Beimer
Franz Schildknecht
Henny Schildknecht
Stefan Nossek
Egon Kling
Else Kling
Tanja Schildknecht-DresslerDr. Ludwig Dressler
Elisabeth Dressler
Carsten Floeter
Vasily Sarikakis
Chris Barnsteg
Elfie Kronmayr
Sigi Kronmayr
Gottlieb Griese
Philo Bennarsch
Joschi Bennarsch
Paul Nolte
Theo Nolte
Herr Floether Der Englaender
Lydia Nolte
Gung Pahm Kien
Gabi Zenker-geb.Skawowski
Helga Beimer Schiller
Hans Beimer
Berta Griese
Marion Beimer
Benny BeimerKlaus Beimer
Franz Schildknecht
Henny Schildknecht
Stefan Nossek
Egon Kling
Else Kling
Tanja Schildknecht-DresslerDr. Ludwig Dressler
Elisabeth Dressler
Frank Dressler
Carsten Floeter
Vasily Sarikakis
Chris Barnsteg
Elfie Kronmayr
Sigi Kronmayr
Gottlieb Griese
Meike Schildknecht Philo Bennarsch
Joschi Bennarsch
Paul Nolte
Theo Nolte
Herr Floether Der Englaender
Figure 24: Graph A99, time points 5, 6 and 7 (first prize).
33
15070
1507315076
15079
15082
15085
15088
15091
15094
15097
15100
15103
15106
15109
15112
15115
1511815121
15124
15127
15130
15133
15136
15139
15142
15145
15148
15151
15154
15157
15160
15163
15166
15169
15172
15175
15178
15181
15184
1518715190
15193
15196
15199
15202
15205
15208
15211
15214
15217
15220
15223
15226
15229
1523215235
15238
15241
15244
15247
15250
15253
15256
15259
Figure
25:G
raphB
99(second
prize).
34
Figure 26: Graph B99 – general view.
35
Figure 27: Graph B99 – different views.
36
XANTHOSINE NUCLEOTIDE
RIBONUCLEIC ACIDDEOXYRIBONUCLEIC ACID
DEOXYGUANOSINE NUCLEOTIDE GUANOSINE NUCLEOTIDE
INOSINE NUCLEOTIDEADENOSINE NUCLEOTIDEDEOXYADENOSINE NUCLEOTIDE
GLUCOSE
TRIACYLGLYCEROLS ISOLEUCINE
CYTOCHROMES
URONIC ACIDS
CELLULOSE
RIBOSE 5-PNDPGLUCOSESUCROSE
FRUCTOSE
GLYCOGEN
STARCH
AMINO SUGARS
ERYTHROSE 4-P
PENTOSES
P-RIBOSYLPP
ASCORBATE
GLUCOSE 6-P
HISTIDINE
PHENYLALANINE
TYROSINE
TRYPTOPHAN
GLYCERALDEHYDE 3-P
CHORISMATE
ASPARTATE
ARGININE
LEUCINE
ALANINE
COBALAMIN
PROTOPORPHYRIN IX
CHLOROPHYLL
HEME
PLANT STEROIDS ISOPRENOIDS
PHOSPOLIPIDS
FATTY ACIDS
3-P GLYCERATE
LIGNIN
ACETYL-CoA
SUCCINATE
CITRATE
PYRUVATE
GLYCEROL
FUMARATE2-OXOGLUTERATE
OXALOACETATE
GLYOXYLATE
HORMONES
FRUCTOSE 6-P
VALINE
SERINE
GLYCINE
CHOLESTEROL
STEROID HORMONES
BILE ACIDS
GLUTAMATE
PROLINE HYDROXYPROLINE
ORNITHINE
LYSINE
THREONINE
METHIONINE
CYSTEINE
UREA
5-AMINOLEVULINATE BILE PIGMENTS
Degradation
Degradation
NAD+
CYTIDINE NUCLEOTIDE
RIBONUCLEIC ACID
DEOXYRIBONUCLEIC ACID
DEOXYCYTIDINE NUCLEOTIDE
URIDINE NUCLEOTIDE DEOXYURIDINE NUCLEOTIDE
DEOXYTHYMIDINE NUCLEOTIDE
Figure
28:G
raphC
99.
37
XANTHOSINE NUCLEOTIDE
RIBONUCLEIC ACIDDEOXYRIBONUCLEIC ACID
DEOXYGUANOSINE NUCLEOTIDE GUANOSINE NUCLEOTIDE
INOSINE NUCLEOTIDEADENOSINE NUCLEOTIDEDEOXYADENOSINE NUCLEOTIDE
GLUCOSE
TRIACYLGLYCEROLS ISOLEUCINE
CYTOCHROMES
URONIC ACIDS
CELLULOSE
RIBOSE 5-PNDPGLUCOSE
SUCROSE
FRUCTOSE
GLYCOGEN
STARCH
AMINO SUGARS
ERYTHROSE 4-P
PENTOSES
P-RIBOSYLPP
ASCORBATE
GLUCOSE 6-P
HISTIDINE
PHENYLALANINE
TYROSINE
TRYPTOPHAN
GLYCERALDEHYDE 3-P
CHORISMATE
ASPARTATE
ARGININE
LEUCINE
ALANINE
COBALAMIN
PROTOPORPHYRIN IX
CHLOROPHYLL
HEME
PLANT STEROIDS ISOPRENOIDS
PHOSPOLIPIDS
FATTY ACIDS
3-P GLYCERATE
LIGNIN
ACETYL-CoA
SUCCINATE
CITRATE
PYRUVATE
GLYCEROL
FUMARATE2-OXOGLUTERATE
OXALOACETATE
GLYOXYLATE
HORMONES
FRUCTOSE 6-P
VALINE
SERINE
GLYCINE
CHOLESTEROL
STEROID HORMONES
BILE ACIDS
GLUTAMATE
PROLINE HYDROXYPROLINE
ORNITHINE
LYSINE
THREONINE
METHIONINE
CYSTEINE
UREA
5-AMINOLEVULINATE BILE PIGMENTS
Degradation
Degradation
NAD+
CYTIDINE NUCLEOTIDE
RIBONUCLEIC ACID
DEOXYRIBONUCLEIC ACID
DEOXYCYTIDINE NUCLEOTIDE
URIDINE NUCLEOTIDE DEOXYURIDINE NUCLEOTIDE
DEOXYTHYMIDINE NUCLEOTIDE
Figure
29:G
raphC
99-
orthogonallayout.
38
Layouts for Graph Drawing Contest 2000
In 2000 Graph Drawing Conference was helt in Colonial Williamsburg (USA) and the con-test 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 re-
moving loops from the graph we got acyclic graph. On the acyclic graph we used standardalgorithms to compute layers and position vertices into layers in order to minimize totallength of lines. Some manual repositioning of vertices was used to avoid some line cross-ings. Vertices having loops are drawn as ellipses other as rectangles. Since graph consists ofseveral 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) formatbesides 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
and to determine the ordering of vertices on the circle we computed�'¡
on the green sub-graph and applied TSP (Travelling Salesman Problem) algorithm on this matrix.
�Y¡3¢ £ ¤N¥§¦¨� © ª ¢ £¦+« ª ¢ ¥§¦ ©© ª ¢ £¦+¬ ª ¢ ¥§¦ © (1)
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 verticeson the circular net. From obtained pictures we can see that neighbouring vertices havesimilar patterns of arcs. Vertices having loops are drawn as boxes (vertices 5 and 11 ingraph A) other as circles. Different gray colors are used to show the frequency of contact:
39
� 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 repre-sentation of graphs A and B. It seems that the matrix representation is more appropriate fordense (parts of) graphs. In the matrix representation the same shadowing is used as in thegraph layout.
The layout was awarded the first prize.The complete report of the contest is available in [9].
40
basic_fstream<char, char_traits<char>>
basic_iostream<char, char_traits<char>>basic_istream<char, char_traits<char>> basic_ios<char, char_traits<char>>
ios_base
locale
basic_ostream<char, char_traits<char>>
basic_filebuf<char, char_traits<char>>
basic_streambuf<char, char_traits<char>>
BrokenRelationException
BuildExceptionlist<string, allocator<PropertyName>>
allocator<PropertyName>
iterator
const_iterator
EntryNotFoundException
FileNotInProjectFileException
Exception
ParentScopeNotFoundException
UnimportantOperationException
UnimportantStatementException
__non_rtti_object bad_typeid
exception
codecvt<wchar_t, char, mbstate_t>
codecvt_base
facet
codecvt<char, char, state_type>
domain_error
logic_errorinvalid_argument
length_error
out_of_range
overflow_error
runtime_errorrange_error
underflow_error
failure
CppModel Model
list<Relation*, allocator<Relation*>>
allocator<Relation*>
iterator const_iterator
set<PropertyName, less<string>, allocator<string>>
allocator<string>
ProjectFile map<string, SectionContents, less<string>, allocator<SectionContents>>allocator<SectionContents>
value_compare
SectionNotFound
VariableNotFound
bad_alloc
bad_cast
bad_exception
basic_istream<wchar_t, char_traits<wchar_t>>basic_ios<wchar_t, char_traits<wchar_t>>
basic_ostream<wchar_t, char_traits<wchar_t>>
num_put<char, _Iter>
numpunct<char>
_Locimp
Array
TypeRef
Type
Entity
Element
Object
SCPos
Class
Record
CppModelFactory ModelFactory
Pointer
PointerToMemberQualifiedType
Struct
TypeDef
Union
ElementType
set<ElementType*, less<ElementType*>, allocator<ElementType*>>
allocator<ElementType*>
ILManager map<ILInstanceKey, ILInstance, less<ILInstanceKey>, allocator<ILInstance>>
allocator<ILInstance>
value_compare
Logmap<int, string, less<int>, allocator<string>>
value_compare
map<string, int, less<string>, allocator<int>>
allocator<int>
value_compare
Measurement map<string, int, less<PropertyName>, allocator<int>> value_compare
Project
set<string, less<string>, allocator<string>>
list<string, allocator<string>> iterator const_iterator
map<string, SourceFile, less<string>, allocator<SourceFile>>
allocator<SourceFile>
value_compare
_Tree<TypeRefHack, value_type, _Kfn, LessByReferencedType, allocator<TypeRefHack>>
allocator<TypeRefHack>
iterator const_iterator
_Tree<TypeRefHack, value_type, _Kfn, LessByReferencedType, allocator<TypeRefHack>> iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<SectionContents>> iterator const_iterator
_Tree<Cell*, value_type, _Kfn, less<Cell*>, allocator<Cell*>> allocator<Cell*>
_Tree<Cell*, value_type, _Kfn, less<Cell*>, allocator<Cell*>> iterator
const_iterator
basic_string<char, char_traits<char>, allocator<char>> allocator<char>
list<Cell*, allocator<Cell*>> iterator const_iterator
stack<Block*, deque<Block*, allocator<Block*>>> deque<Block*, allocator<Block*>> iterator const_iterator
allocator<Block*>
map<Cell*, Cell*, less<Cell*>, allocator<Cell*>> value_compare
multiset<TypeRefHack, LessByReferencedType, allocator<TypeRefHack>>
iterator
Builtin
ClassTemplate
Template
Function
Routine
FunctionTemplate
InNamespace
InScope
Relation
InRecordScope
Member
Field
Method
RoutineType
StaticDataMemberTemplate
Variable
Property
list<PropertyValue, allocator<PropertyValue>>
allocator<PropertyValue>
iterator const_iterator
PropertyValue
_Tree<int, value_type, _Kfn, less<int>, allocator<string>>iterator
_Tree<int, value_type, _Kfn, less<int>, allocator<string>> iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<int>>iterator const_iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<int>> iterator
_Tree<RoutineTypeHack, value_type, _Kfn, LessByParamTypes, allocator<RoutineTypeHack>>
allocator<RoutineTypeHack>
iterator const_iterator
_Tree<PropertyName, value_type, _Kfn, less<string>, allocator<string>>
_Tree<PropertyName, value_type, _Kfn, less<string>, allocator<string>>iterator
_Tree<ElementType*, value_type, _Kfn, less<ElementType*>, allocator<ElementType*>>
allocator<ElementType*>
iterator const_iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<string>> iterator
const_iterator_Tree<string, value_type, _Kfn, less<string>, allocator<string>> iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<ElementType*>>
_Tree<string, value_type, _Kfn, less<string>, allocator<ElementType*>> iterator
const_iterator
_Tree<ILInstanceKey, value_type, _Kfn, less<ILInstanceKey>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<ILInstanceKey>, allocator<ILInstance>> iterator
const_iterator
_Tree<string, value_type, _Kfn, less<ILInstanceKey>, allocator<int>>
_Tree<string, value_type, _Kfn, less<ILInstanceKey>, allocator<int>>iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<string>> iteratorconst_iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<string>>iterator
_Tree<string, value_type, _Kfn, less<string>, allocator<SourceFile>>allocator<SourceFile>
iterator const_iterator
_Tree<ILInstanceKey, value_type, _Kfn, less<string>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<string>, allocator<ILInstance>>iterator
_Tree<STD_Ptr<Cell>, value_type, _Kfn, CellLessByElementID, allocator<STD_Ptr<Cell>>> allocator<STD_Ptr<Cell>>
_Tree<STD_Ptr<Cell>, value_type, _Kfn, CellLessByElementID, allocator<STD_Ptr<Cell>>>iterator const_iterator
_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<PropertyName>> iterator
const_iterator_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<PropertyName>>
iterator
_Tree<int, value_type, _Kfn, less<int>, allocator<PropertyName>> iterator
_Tree<int, value_type, _Kfn, less<int>, allocator<PropertyName>> iterator
_Tree<string, value_type, _Kfn, less<PropertyName>, allocator<int>> iterator
_Tree<string, value_type, _Kfn, less<PropertyName>, allocator<int>> iterator
_Tree<void*, value_type, _Kfn, less<void*>, allocator<Entity*>>allocator<Entity*>
iterator
const_iterator_Tree<void*, value_type, _Kfn, less<void*>, allocator<Entity*>>iterator
_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<Property>>allocator<Property>
iterator
const_iterator_Tree<PropertyName, value_type, _Kfn, less<PropertyName>, allocator<Property>>
iterator
_Tree<ILInstanceKey, value_type, _Kfn, less<PropertyName>, allocator<ILInstance>>
_Tree<ILInstanceKey, value_type, _Kfn, less<PropertyName>, allocator<ILInstance>>
iterator
_Tree<PropertyName, value_type, _Kfn, less<string>, allocator<PropertyName>>
_Tree<PropertyName, value_type, _Kfn, less<string>, allocator<PropertyName>>iterator
const_iterator
list<Entity*, allocator<Entity*>> iterator const_iterator
allocator<Entity*>
list<Element*, allocator<Element*>>
allocator<Element*>
iterator const_iterator
list<TempResult, allocator<TempResult>>
allocator<TempResult>
iterator const_iterator
TempResult
list<STD_Ptr<TemplateParameter>, allocator<STD_Ptr<TemplateParameter>>>
allocator<STD_Ptr<TemplateParameter>>
iterator const_iterator
STD_Ptr<TemplateParameter>
list<BaseClass*, allocator<BaseClass*>>
allocator<BaseClass*>
iterator const_iterator
allocator<BaseClass*>
list<Constant*, allocator<Constant*>>
allocator<Constant*>
iterator const_iterator
list<Actual, allocator<Actual>>
allocator<Actual>
iterator const_iterator
reverse_iterator<iterator, value_type, reference, reference*, difference_type> iteratorconst_iterator
reference
map<string, ElementType*, less<string>, allocator<ElementType*>> value_compare
map<string, int, less<ILInstanceKey>, allocator<int>> value_compare
map<string, string, less<string>, allocator<string>>value_compare
map<ILInstanceKey, ILInstance, less<string>, allocator<ILInstance>>value_compare
map<int, string, less<int>, allocator<PropertyName>> value_compare
map<void*, Entity*, less<void*>, allocator<Entity*>>value_compare
map<PropertyName, Property, less<PropertyName>, allocator<Property>>
value_compare
map<ILInstanceKey, ILInstance, less<PropertyName>, allocator<ILInstance>> value_compare
multiset<RoutineTypeHack, LessByParamTypes, allocator<RoutineTypeHack>>
set<STD_Ptr<Cell>, CellLessByElementID, allocator<STD_Ptr<Cell>>>
set<PropertyName, less<PropertyName>, allocator<PropertyName>>
set<PropertyName, less<string>, allocator<PropertyName>>
vector<_Bool, _Bool_allocator>
ConcretePrimitiveQuery
PrimitiveQuery
Query
list<ColumnDef, allocator<ColumnDef>>
allocator<ColumnDef>iterator const_iterator
ColumnDef
DummyRelation
EntitiesByTypeQuery
RelationsByTypeQuery
iterator
iterator
iterator
iterator
Accessor
Block list<STD_Ptr<Block>, allocator<STD_Ptr<Block>>>allocator<STD_Ptr<Block>>
iterator const_iterator
allocator<STD_Ptr<Block>>STD_Ptr<Block>
STD_Ptr<Block>
CallFieldAccess
Friend
HasType
Inheritance
LocalVariableOfType
LocallyUsedType
NameSpace
Parameter
ReturnType
TemplateInstance
TypeUsedInTypeRef
basic_streambuf<wchar_t, char_traits<wchar_t>>
reverse_iterator<const_iterator, value_type, const_reference, const_reference*, difference_type>
ParallelQuerylist<Query*, allocator<Query*>>
allocator<Query*>iterator const_iterator
RecursiveQuery
Scopemultiset<STD_Ptr<Entity>, LessByName, allocator<STD_Ptr<Entity>>> allocator<STD_Ptr<Entity>>
set<STD_Ptr<Scope>, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>> allocator<STD_Ptr<Scope>>
SerialQuery
Constant
TemplateParameter_Tree<STD_Ptr<Scope>, value_type, _Kfn, less<STD_Ptr<Scope>>, allocator<STD_Ptr<Scope>>> iterator const_iterator
_Tree<STD_Ptr<Entity>, value_type, _Kfn, LessByName, allocator<STD_Ptr<Entity>>> iterator const_iterator
Figure
30:C
omplete
layoutofH
imsoltgraph
A00.
41
0
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
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
4950
51
52
53
54
55
56
57
58
59
60
61
62
63
64
656667
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
8687
88
89
90
91
9293
94
95
96
97
98
99
Figure 31: Graph B00-A - circular layout (first prize).
42
0
1
2
3
4
5
6
7
8
9
1011
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Figure 32: Graph B00-B - circular layout.
43
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
9 G
reen
1
6 G
reen
1
7 G
reen
8
Gre
en
11
Gre
en
13
Gre
en
7 G
reen
6
Gre
en
2 G
reen
4
Gre
en
5 G
reen
1
9 G
reen
6
2 G
reen
1
2 G
reen
1
8 G
reen
1
4 G
reen
1
Gre
en
0 G
reen
3
Gre
en
20
Gre
en
15
Gre
en
10
Gre
en
66
Blu
e 7
6 B
lue
86
Blu
e 9
2 B
lue
94
Blu
e 6
7 B
lue
72
Blu
e 8
0 B
lue
68
Blu
e 8
2 B
lue
63
Blu
e 7
3 B
lue
81
Blu
e 10
0 B
lue
79
Blu
e 9
7 B
lue
74
Blu
e 7
7 B
lue
78
Blu
e 9
1 B
lue
85
Blu
e 7
1 B
lue
99
Blu
e 9
0 B
lue
64
Blu
e 9
5 B
lue
69
Blu
e 7
0 B
lue
75
Blu
e 8
3 B
lue
87
Blu
e 8
9 B
lue
93
Blu
e 9
6 B
lue
84
Blu
e 6
5 B
lue
88
Blu
e 9
8 B
lue
21
Yel
low
47
Yel
low
33
Yel
low
55
Yel
low
39
Yel
low
30
Yel
low
57
Yel
low
24
Yel
low
32
Yel
low
51
Yel
low
48
Yel
low
26
Yel
low
22
Yel
low
61
Yel
low
49
Yel
low
31
Yel
low
40
Yel
low
56
Yel
low
25
Yel
low
44
Yel
low
60
Yel
low
37
Yel
low
41
Yel
low
23
Yel
low
34
Yel
low
38
Yel
low
45
Yel
low
46
Yel
low
50
Yel
low
58
Yel
low
52
Yel
low
53
Yel
low
43
Yel
low
36
Yel
low
54
Yel
low
28
Yel
low
35
Yel
low
29
Yel
low
59
Yel
low
42
Yel
low
27
Yel
low
Figure 33: Matrix representation of graph B00-B.
44
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
3 G
reen
13
Gre
en
11 G
reen
1
Gre
en
0 G
reen
17
Gre
en
9 G
reen
2
Gre
en
12 G
reen
81
Gre
en
5 G
reen
15
Gre
en
14 G
reen
18
Gre
en
10 G
reen
16
Gre
en
4 G
reen
8
Gre
en
7 G
reen
6
Gre
en
92 B
lue
91 B
lue
82 B
lue
83 B
lue
84 B
lue
85 B
lue
86 B
lue
87 B
lue
88 B
lue
93 B
lue
89 B
lue
96 B
lue
97 B
lue
98 B
lue
99 B
lue
90 B
lue
94 B
lue
95 B
lue
78 Y
ello
w
64 Y
ello
w
25 Y
ello
w
32 Y
ello
w
74 Y
ello
w
26 Y
ello
w
27 Y
ello
w
52 Y
ello
w
55 Y
ello
w
23 Y
ello
w
60 Y
ello
w
62 Y
ello
w
24 Y
ello
w
20 Y
ello
w
77 Y
ello
w
46 Y
ello
w
61 Y
ello
w
80 Y
ello
w
28 Y
ello
w
39 Y
ello
w
34 Y
ello
w
43 Y
ello
w
72 Y
ello
w
22 Y
ello
w
57 Y
ello
w
69 Y
ello
w
70 Y
ello
w
65 Y
ello
w
66 Y
ello
w
67 Y
ello
w
31 Y
ello
w
37 Y
ello
w
42 Y
ello
w
71 Y
ello
w
19 Y
ello
w
41 Y
ello
w
53 Y
ello
w
59 Y
ello
w
73 Y
ello
w
29 Y
ello
w
79 Y
ello
w
40 Y
ello
w
21 Y
ello
w
36 Y
ello
w
48 Y
ello
w
49 Y
ello
w
50 Y
ello
w
51 Y
ello
w
58 Y
ello
w
68 Y
ello
w
44 Y
ello
w
45 Y
ello
w
54 Y
ello
w
75 Y
ello
w
33 Y
ello
w
63 Y
ello
w
56 Y
ello
w
30 Y
ello
w
76 Y
ello
w
47 Y
ello
w
38 Y
ello
w
35 Y
ello
w
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
9 G
reen
1
6 G
reen
1
7 G
reen
8
Gre
en
11
Gre
en
13
Gre
en
7 G
reen
6
Gre
en
2 G
reen
4
Gre
en
5 G
reen
1
9 G
reen
6
2 G
reen
1
2 G
reen
1
8 G
reen
1
4 G
reen
1
Gre
en
0 G
reen
3
Gre
en
20
Gre
en
15
Gre
en
10
Gre
en
66
Blu
e 7
6 B
lue
86
Blu
e 9
2 B
lue
94
Blu
e 6
7 B
lue
72
Blu
e 8
0 B
lue
68
Blu
e 8
2 B
lue
63
Blu
e 7
3 B
lue
81
Blu
e 10
0 B
lue
79
Blu
e 9
7 B
lue
74
Blu
e 7
7 B
lue
78
Blu
e 9
1 B
lue
85
Blu
e 7
1 B
lue
99
Blu
e 9
0 B
lue
64
Blu
e 9
5 B
lue
69
Blu
e 7
0 B
lue
75
Blu
e 8
3 B
lue
87
Blu
e 8
9 B
lue
93
Blu
e 9
6 B
lue
84
Blu
e 6
5 B
lue
88
Blu
e 9
8 B
lue
21
Yel
low
47
Yel
low
33
Yel
low
55
Yel
low
39
Yel
low
30
Yel
low
57
Yel
low
24
Yel
low
32
Yel
low
51
Yel
low
48
Yel
low
26
Yel
low
22
Yel
low
61
Yel
low
49
Yel
low
31
Yel
low
40
Yel
low
56
Yel
low
25
Yel
low
44
Yel
low
60
Yel
low
37
Yel
low
41
Yel
low
23
Yel
low
34
Yel
low
38
Yel
low
45
Yel
low
46
Yel
low
50
Yel
low
58
Yel
low
52
Yel
low
53
Yel
low
43
Yel
low
36
Yel
low
54
Yel
low
28
Yel
low
35
Yel
low
29
Yel
low
59
Yel
low
42
Yel
low
27
Yel
low
Figure
34:M
atrixrepresentation
ofnon
empty
partofgraphs
B00-A
andB
00-B.
45
Layouts for Graph Drawing Contest 2001
In 2001 Graph Drawing Conference was helt in Vienna and the contest was organised byFranz Brandenburg. Rules and data are described at:
http://www.ads.tuwien.ac.at/gd2001/
Graph A01
In a given set of units¶
(articles, books, works, . . . ) we introduce a ¹�ºT»bºT¼k½ relation ¾À¿¶ÂÁö ľÆÅ�ÇÈÅ cites
Äwhich determines a citation network
¢É¶�¤ ¾ ¦ . A citing relation is usually irreflexive, ÊÄ ¶Ë´�Ì Ä ¾
Ä, and (almost) acyclic, Ê
Ä @¶ ÊÍ IN� ´�Ì Ä ¾8Î
Ä. 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 itsimportance or weight. These values are used afterwards to determine the essential substruc-tures in the network. Hummon and Doreian (1989, 1990) [1, 2, 3] proposed three methodsof assigning weights Ï ´ ¾@Ð IR
�Ñ to arcs:
46
� NPCC method: Ï � ¢ £Ò¤N¥�¦�� © ¾ÔÓ � ¢ £¦ ©1ÕH© ¾ ¢ ¥§¦ ©� Paths count method: Ï ¡3¢ £Ò¤N¥�¦Ö� ª ¢ £Ò¤N¥§¦, where ª ¢ £Ò¤N¥�¦
denotes the number ofdifferent paths from ׳ØoÙ�¾ to ׳Ú1Ûܾ (or from � to » ) through the arc
¢ £Ò¤N¥�¦� SPLC method: ÏÞÝ ¢ £ ¤N¥§¦ß� ªÖà ¢ £Ò¤N¥§¦ , where ªÖà ¢ £Ò¤N¥§¦ equals to ª ¢ £Ò¤N¥�¦
from pathscount method over the network
¢É¶�¤ ¾ à ¦ , ¾ à ´���¢ ¾ ¬á± � ·1¦âÁ�¢É¶äãK± � ¤ » ·1¦The last two methods are efficiently (Batagelj, 1991, 1994) [4] implemented in Pajek
and can be applied also on (very) large acyclic networks. Let ª Ó ¢ ¥�¦ denotes the numberof different paths from � to
¥, and ª � ¢ ¥§¦ denotes the number of different paths from
¥to» . Then ª ¢ £Ò¤N¥�¦u� ª Ó ¢ £¦ Õ�ª � ¢ ¥�¦:¤�¢ £Ò¤N¥§¦Ü ¾ .ª and ªÖà are flows in the network since they obey the Kirchoff’s node law:
For every node¥
in a citation network¢É¶�¤ ¾ ¦ in standard form it holds
incoming flow�
outgoing flow
Therefore the total flow through the citation network equals ª ¢ » ¤ � ¦ . This gives us a naturalway to normalize the weights
Ï ¢ £Ò¤N¥�¦u� ª ¢ £Ò¤N¥�¦ª ¢ » ¤ � ¦ å æ�ç Ï ¢ £ ¤N¥§¦ ç²è
If é is a minimal cut-set it also holds êë�ì-í î:ïZð�ñ Ï ¢ £Ò¤N¥�¦�� è
We can assign weights also to vertices
Ï ¢ ¥�¦u�áª 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 311vertices. 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 byan erroneous arc ( GD94/143 Eades, GD98/423 Eades). After reversing it 4 small strongcomponents remained, corresponding to mutual references
±GD94/286 Garg, GD94/298
Papakostas·,±
GD94/328 Di Battista, GD94/340 Bose, GD94/352 ElGindy·,±
GD95/8Alt, 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:
47
Each paper from a strong component is duplicated with its ’preprint’ version. The papersinside strong component cite preprints.
The pictures were exported as nested partitions into SVG format that allows interactivedisplay of different slices – subgraphs induced by arcs with weights larger than a thresholdvalue. 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 ver-
tices). The vertices are put in layers (vertical position and color of vertices) according tothe years of publication. The placement of vertices inside the layer was determined by lo-cal optimization. The width and the color density of an arc and the size of a vertex areproportional to their citation weights.
The second and the third picture display the main parts (slices) of the citation networkat threshold values 0.02 and 0.05. The red arcs belong to the ’main path’.
48
Figure 35: Graph A – complete graph.
49
Figure 36: Graph A – level 0.02.
50
Figure 37: Graph A – level 0.05.
51
Graph B
To obtain the ’central symmetric’ picture of graph B energy drawing was used, followedby manual grid positioning of vertices. To save the space the lower part of the picture wasmanually mirrored across the vertical axis.
P0
T8+
P-2
2
P0
P-22
T8+
P+
22
T9+
P-2
2
T9+
T9+
T8-
T8+
T9+
T9-
T8-
T8+
T9+
T9-
T8-
T8+
T9-T
9+
T8-
T9-
T9+
T0+
T9+
P-90
T9+ T8+
P-6
0
P+90
T9+
T8+T8+
T8+
+90 posturn right
turn right equalizer
0 pos turn left equalizer
+22 pos
turn left+22 - +90 intermediate
0 - +22 intermediate
turn right equalizer
-22 pos
turn right
-90 pos turn left
-60 pos
turn left equalizer
0 - -22 intermediate
-22 - -90 intermediate
Figure 38: Graph B – ’central symmetric’.
Graph C
Graph C is an acyclic directed graph. Such graphs can be topologically sorted. The corre-sponding adjacency matrix has zero lower triangle and diagonal. Since the graph is ratherdense we decided to use the matrix representation to visualize the graph structure. Layersare represented by blocks divided by blue lines.
52
P0
T8+
P-2
2P
0P
-22
T8+
P+
22T
9+P
-22
T9+
T9+
T8-
T8+
T9+
T9-
T8-
T8+
T9+
T9-
T8-
T8+
T9-T
9+
T8-
T9-
T9+
T0+
T9+
P-90
T9+
T8+ P
-60
P+90
T9+
T8+T8+
T8+
+90 posturn right
turn right equalizer
0 posturn left equalizer
+22 pos
turn left+22 - +90 intermediate
0 - +22 intermediate
turn right equalizer
-22 pos
turn right
-90 posturn left
-60 pos
turn left equalizer
0 - -22 intermediate
-22 - -90 intermediate
Figure 39: Graph B – mirror.
53
Pajek - shadow [0.00,1.00]
RGCLGNV1V2V3VPPIPV3AMDPMIPPOMTV4tV4VOTVIPLIPMSTFSTPIT7aFEFSTPpCIT46STPaAITOFC36TFTHERHC
RG
CLG
NV
1V
2V
3V
PP
IPV
3AM
DP
MIP
PO
MT
V4t
V4
VO
TV
IPLI
PM
ST
FS
TP
IT7a F
EF
ST
Pp
CIT
46 ST
Pa
AIT
OF
C36 T
FT
HE
RH
C
Figure 40: Graph C – matrix representation.
REFERENCES 54
References
[1] Hummon N.P., Doreian P. (1989): Connectivity in a Citation Network: The Develop-ment of DNA Theory. Social Networks, 11 39-63.
[2] Hummon N.P., Doreian P. (1990): Computational Methods for Social Network Anal-ysis. Social Networks, 12 273-288.
[3] Hummon N.P., Doreian P., Freeman L.C. (1990): Analyzing the Structure of theCentrality-Productivity Literature Created Between 1948 and 1979. Knowledge: Cre-ation, Diffusion, Utilization, 11(4), 459-480.
[4] Batagelj V. (1991): An Efficient Algorithm for Citation Networks Analysis. Presentedat EASST’94, Budapest, Hungary, August 28-31, 1994. First presented at the Seminaron social networks. University of Pittsburgh, January 1991.
[5] Batagelj V., Doreian P., and Ferligoj A. (1992): An Optimizational Approach to Regu-lar Equivalence. Social Networks 14, 121-135.
[6] Brandenburg, F. J. (1996): Graph Drawing. Proceedings of Symposium on GraphDrawing, GD95, Passau, Germany, September 1995, Springer-Verlag, Lecture Notesin Computer Science, vol. 1027, 224-233.
[7] DiBattista, G. (1998): Graph Drawing. Proceedings of Symposium on Graph Draw-ing, GD97, Rome, Italy, September 1997, Springer-Verlag, Lecture Notes in ComputerScience, vol. 1353, 438-445.
[8] Kratochvil, J. (1999): Graph Drawing. Proceedings of Symposium on Graph Draw-ing, 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 Draw-ing, 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 Notesin Computer Science, vol. 1190, 129-138.