Chapter 10
Combining directed and
signed embeddings
We now show how the layer approach and compositions can be used to model networks that have edges that are both signed (with positive and negative weights) and
directed. So, for example, we will be able to model the situation where A has a
positive relationship with B, but B has a negative relationship with A.
Intelligence, terrorism and law-enforcement applications, in particular, are characterized by asymmetric relationships (command-and-control or flow of information)
and by relationships with both allies and foes. Understanding the social dynamics
of a group, or the ecosystem of interactions among groups requires social network
analysis for networks in which the edges are both signed and directed.
In this chapter we take the signed embedding technique, the directed embedding technique, and the composition of layered models technique and show how to
use them to embed directed, signed networks. Properties of the network can be understood from visualizations; we also define a measure that highlights nodes with
unusual roles.
10.1 Composition of directed and signed layer
models
As before, the strategy for embedding based on both sign and direction is to take
the information implicit in the network edges (direction and sign) and encode it by
introducing multiple versions for each node.
First, multiple versions of each node are created, one connected to the positive
edges, and one to the negative edges. Then, each node is replaced by two versions,
one coding for its incoming edges and the other for its outgoing edges, as in the
new directed network construction. All of the edges connecting versions are undirected, since the directional information is coded in the pattern of connections of
these edges. Each node of the original graph is therefore replaced by four versions
with these connections: incoming negative edges, outgoing negative edges, incom139
Combining directed and
signed embeddings
We now show how the layer approach and compositions can be used to model networks that have edges that are both signed (with positive and negative weights) and
directed. So, for example, we will be able to model the situation where A has a
positive relationship with B, but B has a negative relationship with A.
Intelligence, terrorism and law-enforcement applications, in particular, are characterized by asymmetric relationships (command-and-control or flow of information)
and by relationships with both allies and foes. Understanding the social dynamics
of a group, or the ecosystem of interactions among groups requires social network
analysis for networks in which the edges are both signed and directed.
In this chapter we take the signed embedding technique, the directed embedding technique, and the composition of layered models technique and show how to
use them to embed directed, signed networks. Properties of the network can be understood from visualizations; we also define a measure that highlights nodes with
unusual roles.
10.1 Composition of directed and signed layer
models
As before, the strategy for embedding based on both sign and direction is to take
the information implicit in the network edges (direction and sign) and encode it by
introducing multiple versions for each node.
First, multiple versions of each node are created, one connected to the positive
edges, and one to the negative edges. Then, each node is replaced by two versions,
one coding for its incoming edges and the other for its outgoing edges, as in the
new directed network construction. All of the edges connecting versions are undirected, since the directional information is coded in the pattern of connections of
these edges. Each node of the original graph is therefore replaced by four versions
with these connections: incoming negative edges, outgoing negative edges, incom139