xiv
List of Figures
5.14
Network embedding of the Panama Papers 44th component — directed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.15
Network embedding of the Panama Papers 44th component —
undirected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.16
Network embeddings of the Panama Papers 10th component, threshold 300 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.17
Edges between version, 10th component . . . . . . . . . . . . . . 67
6.1
Added edges between the multiple versions of a single node . . . 70
6.2
Chung directed embedding of the typed Florentine families . . . . 72
6.3
Our directed embedding of the typed Florentine families . . . . . 73
6.4
Zoom-in of the Medici nodes . . . . . . . . . . . . . . . . . . . 74
6.5
Our directed embedding of the Chalonero network (untyped edges) 76
6.6
Chung directed embedding of the typed Chalonero network . . . 77
6.7
Our directed embedding of the typed Chalonero network . . . . . 78
6.8
Our directed embedding of the typed Stupor Mundi network . . . 80
7.1
The general embedding of the Caviar network . . . . . . . . . . . 86
7.2
Zoom-in the general embedding of the Caviar network . . . . . . 87
7.3
The embedding of the Caviar network with the 11 time periods . . 88
7.4
The embedding of the 5 key participants over time . . . . . . . . 88
7.5
Growth of the embedded network over time . . . . . . . . . . . . 91
7.6
Average diameter of the undirected network over time . . . . . . 92
7.7
Trajectories — Chung’s embedding . . . . . . . . . . . . . . . . 93
7.8
Trajectories — our embedding . . . . . . . . . . . . . . . . . . . 93
8.1
Unnormalized signed graph embedding of a toy dataset . . . . . . 100
8.2
Graph cuts of a sample graph . . . . . . . . . . . . . . . . . . . 101
8.3
Normalized signed graph embedding of a toy data . . . . . . . . 103
8.4
Embeddings of the enemy of my enemy . . . . . . . . . . . . . . 106
8.5
The embeddings of the tribes . . . . . . . . . . . . . . . . . . . . 108
8.6
The embeddings of the Sampson monastery network . . . . . . . 110
8.7
The embeddings of the ACLED violent groups . . . . . . . . . . 112
8.8
The ratio values of the ACLED embedding . . . . . . . . . . . . 113
8.9
The ratio values of the Epinions embeddings (forest-fire sampling) 114
8.10
The ratio values of the Epinions embeddings (random-walk sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.11
The ratio values of the Slashdot embeddings (forest-fire sampling) 116
8.12
The Slashdot embeddings with 100 nodes (forest-fire sampling) . 117
8.13
The ratio values of the Slashdot embeddings (random-walk sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.1
Two ways to add negative edges . . . . . . . . . . . . . . . . . . 123
9.2
Applying GBE to two toy datasets . . . . . . . . . . . . . . . . . 127
9.3
Plot of average error as a function of parameters . . . . . . . . . 128
List of Figures
5.14
Network embedding of the Panama Papers 44th component — directed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.15
Network embedding of the Panama Papers 44th component —
undirected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.16
Network embeddings of the Panama Papers 10th component, threshold 300 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.17
Edges between version, 10th component . . . . . . . . . . . . . . 67
6.1
Added edges between the multiple versions of a single node . . . 70
6.2
Chung directed embedding of the typed Florentine families . . . . 72
6.3
Our directed embedding of the typed Florentine families . . . . . 73
6.4
Zoom-in of the Medici nodes . . . . . . . . . . . . . . . . . . . 74
6.5
Our directed embedding of the Chalonero network (untyped edges) 76
6.6
Chung directed embedding of the typed Chalonero network . . . 77
6.7
Our directed embedding of the typed Chalonero network . . . . . 78
6.8
Our directed embedding of the typed Stupor Mundi network . . . 80
7.1
The general embedding of the Caviar network . . . . . . . . . . . 86
7.2
Zoom-in the general embedding of the Caviar network . . . . . . 87
7.3
The embedding of the Caviar network with the 11 time periods . . 88
7.4
The embedding of the 5 key participants over time . . . . . . . . 88
7.5
Growth of the embedded network over time . . . . . . . . . . . . 91
7.6
Average diameter of the undirected network over time . . . . . . 92
7.7
Trajectories — Chung’s embedding . . . . . . . . . . . . . . . . 93
7.8
Trajectories — our embedding . . . . . . . . . . . . . . . . . . . 93
8.1
Unnormalized signed graph embedding of a toy dataset . . . . . . 100
8.2
Graph cuts of a sample graph . . . . . . . . . . . . . . . . . . . 101
8.3
Normalized signed graph embedding of a toy data . . . . . . . . 103
8.4
Embeddings of the enemy of my enemy . . . . . . . . . . . . . . 106
8.5
The embeddings of the tribes . . . . . . . . . . . . . . . . . . . . 108
8.6
The embeddings of the Sampson monastery network . . . . . . . 110
8.7
The embeddings of the ACLED violent groups . . . . . . . . . . 112
8.8
The ratio values of the ACLED embedding . . . . . . . . . . . . 113
8.9
The ratio values of the Epinions embeddings (forest-fire sampling) 114
8.10
The ratio values of the Epinions embeddings (random-walk sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.11
The ratio values of the Slashdot embeddings (forest-fire sampling) 116
8.12
The Slashdot embeddings with 100 nodes (forest-fire sampling) . 117
8.13
The ratio values of the Slashdot embeddings (random-walk sampling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.1
Two ways to add negative edges . . . . . . . . . . . . . . . . . . 123
9.2
Applying GBE to two toy datasets . . . . . . . . . . . . . . . . . 127
9.3
Plot of average error as a function of parameters . . . . . . . . . 128