List of Figures
2.1
Illustration for within-layer connection and between-layer connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2
The embedding of a simple graph with typed edges . . . . . . . . 13
3.1
The eigendecomposition of the cloud of points corresponding to
graph nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1
The embedding of the Florentine families based on personal relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2
The embedding of the Florentine families based on financial relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3
The embedding of Florentine families ignoring edge types . . . . 37
4.4
Embedding of Florentine families with typed edges . . . . . . . . 38
4.5
Zooming in to the embedded Florentine families with typed edges 39
4.6
Zooming in even further . . . . . . . . . . . . . . . . . . . . . . 40
5.1
A circle graph Laplacian embedding . . . . . . . . . . . . . . . . 45
5.2
The difference between symmetric and asymmetric flow . . . . . 50
5.3
Embeddings of synthetic datasets . . . . . . . . . . . . . . . . . 51
5.4
Network embeddings of UK university faculties . . . . . . . . . . 52
5.5
Network embeddings of Florentine families . . . . . . . . . . . . 54
5.6
Network embeddings of Macaque monkey visuotactile brain . . . 56
5.7
The basic structure of tax avoidance using a shell company . . . . 58
5.8
The adjacency matrix of the largest connected component . . . . 58
5.9
Network embedding of the Panama Papers 6th component — directed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.10
Network embedding of the Panama Papers 6th component — undirected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.11
Network embedding of the Panama Papers 2nd component . . . . 61
5.12
Network embedding of the Panama Papers 41st component — directed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.13
Network embedding of the Panama Papers 41st component —
undirected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
xiii
2.1
Illustration for within-layer connection and between-layer connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2
The embedding of a simple graph with typed edges . . . . . . . . 13
3.1
The eigendecomposition of the cloud of points corresponding to
graph nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1
The embedding of the Florentine families based on personal relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2
The embedding of the Florentine families based on financial relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3
The embedding of Florentine families ignoring edge types . . . . 37
4.4
Embedding of Florentine families with typed edges . . . . . . . . 38
4.5
Zooming in to the embedded Florentine families with typed edges 39
4.6
Zooming in even further . . . . . . . . . . . . . . . . . . . . . . 40
5.1
A circle graph Laplacian embedding . . . . . . . . . . . . . . . . 45
5.2
The difference between symmetric and asymmetric flow . . . . . 50
5.3
Embeddings of synthetic datasets . . . . . . . . . . . . . . . . . 51
5.4
Network embeddings of UK university faculties . . . . . . . . . . 52
5.5
Network embeddings of Florentine families . . . . . . . . . . . . 54
5.6
Network embeddings of Macaque monkey visuotactile brain . . . 56
5.7
The basic structure of tax avoidance using a shell company . . . . 58
5.8
The adjacency matrix of the largest connected component . . . . 58
5.9
Network embedding of the Panama Papers 6th component — directed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.10
Network embedding of the Panama Papers 6th component — undirected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.11
Network embedding of the Panama Papers 2nd component . . . . 61
5.12
Network embedding of the Panama Papers 41st component — directed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.13
Network embedding of the Panama Papers 41st component —
undirected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
xiii