5.3. Applications of directed networks
51
(a) Map of two joined circles
(b) Embedding using the new directed
approach
(c) Embedding using Chung’s directed
approach
(d) Shaded by average normalized
edge length in the new embedding
(e) Shaded by in-out edge length in the
new embedding
Figure 5.3: Embeddings of synthetic datasets
Figure 5.5(a) shows the directed graph embedding using Chung’s directed approach in three dimensions. There is a clear separation between the Medici group
and oligarch families, except for Guicciardini and Tornabuoni. Medici is located in
the center and is the key family that connects the two blocs. The Medici group forms
three long arms in the embedding.
This embedding shows that the oligarch families are well connected, since they
are all placed close to one another; but the Medici group is only weakly connected.
This embedding is consistent with historians’ views.
51
(a) Map of two joined circles
(b) Embedding using the new directed
approach
(c) Embedding using Chung’s directed
approach
(d) Shaded by average normalized
edge length in the new embedding
(e) Shaded by in-out edge length in the
new embedding
Figure 5.3: Embeddings of synthetic datasets
Figure 5.5(a) shows the directed graph embedding using Chung’s directed approach in three dimensions. There is a clear separation between the Medici group
and oligarch families, except for Guicciardini and Tornabuoni. Medici is located in
the center and is the key family that connects the two blocs. The Medici group forms
three long arms in the embedding.
This embedding shows that the oligarch families are well connected, since they
are all placed close to one another; but the Medici group is only weakly connected.
This embedding is consistent with historians’ views.