In the previous chapter, we focused on actors: how to group them into communities. In this chapter, we focus on edges.

One of the most popular data mining tasks for social networks is link (or edge) prediction: given the current status of a social network, which edges are likely to appear at a later time? This problem was originally defined for single-layer networks and is related to the topic of network evolution that we present in Chapter 8. In both cases, there is an underlying assumption about the social dynamics that lead to the appearance of new edges, for example, the fact that actors with many edges have a higher probability of receiving even more edges, or the fact that actors with many common neighbors have a higher probability of becoming neighbors themselves. However, with social network evolution models, the objective is typically the generation of synthetic social networks having some desired global properties, for example, a given clustering coefficient or degree distribution. In the case of edge prediction, the objective is to infer local edges, that is, to predict if an edge is going to appear between two given nodes, or to rank currently disconnected pairs of nodes according to the likelihood that they will become connected.We discuss the edge prediction problem in Section 7.1.

Although edge prediction for multilayer social networks can be seen as a direct extension of existing methods for single-layer networks, a specific kind of knowledge that only makes sense when we have multiple layers is the existence of layer correlations. In Chapter 2 we described different measures to detail the relationship between some predefined layers. However, when many layers exist, we may need automated methods to identify the specific combinations of layers showing significant correlations. We cover this problem in Section 7.2.

Edge Prediction

Edge prediction, as defined by Liben-Nowell and Kleinberg (2003), addresses the following question: which edges are going to be present at time t1 given the edges existing at a previous time t0? Figure 7.1 shows the work layer of our running example at two different points in time: in the figure, three new edges appear and one disappears at time t1.