36
Chapter 4. Modelling relationships of different types
Figure 4.2: The embedding of the Florentine families based on financial relationships
and undirected edges
Edge prediction
Edge prediction uses the structure of the embedding and, in particular, the existence
of Euclidean distance as an encoding of similarity, to predict pairs of nodes that are
not already connected but for which an edge is plausible.
Edge prediction is a nice illustration of how social networks integrate local
information into a global whole which then has local implications. The two nodes
for which a joining edge is recommended are detected as similar because of all of
the other nodes and edges in the entire social network, and their mutual similarities.
Although the embedding is quite cluttered, we can get insights by computing
the pairwise distances. One of the shortest distances is between the Pepi and Scambrilla families. Castellani is the only family that has a relationship (marriage) with
them. Since the Pepi and Scambrilla families have the same connections, they are
embedded in the same place, suggesting that they play effectively equivalent roles in
the social system of Florence and so should have an edge between them.
The Strozzi and Medici families are quite remote from one another in this
social network, but the embedding suggests that, if they make a connection, it is significantly more likely to be a marriage connection rather than a financial connection
— the distances between them in the embedding are 0.124 (personal) and 0.145 (financial). That is indeed what happened: the Strozzis married into the Medicis, but
not until years later.
Chapter 4. Modelling relationships of different types
Figure 4.2: The embedding of the Florentine families based on financial relationships
and undirected edges
Edge prediction
Edge prediction uses the structure of the embedding and, in particular, the existence
of Euclidean distance as an encoding of similarity, to predict pairs of nodes that are
not already connected but for which an edge is plausible.
Edge prediction is a nice illustration of how social networks integrate local
information into a global whole which then has local implications. The two nodes
for which a joining edge is recommended are detected as similar because of all of
the other nodes and edges in the entire social network, and their mutual similarities.
Although the embedding is quite cluttered, we can get insights by computing
the pairwise distances. One of the shortest distances is between the Pepi and Scambrilla families. Castellani is the only family that has a relationship (marriage) with
them. Since the Pepi and Scambrilla families have the same connections, they are
embedded in the same place, suggesting that they play effectively equivalent roles in
the social system of Florence and so should have an edge between them.
The Strozzi and Medici families are quite remote from one another in this
social network, but the embedding suggests that, if they make a connection, it is significantly more likely to be a marriage connection rather than a financial connection
— the distances between them in the embedding are 0.124 (personal) and 0.145 (financial). That is indeed what happened: the Strozzis married into the Medicis, but
not until years later.