Bi-Pattern Mining of Two Mode and Directed Networks.

In two-mode networks there are two kinds of vertices, i.e objects, each being possibly described with a proper attribute set. This means that to select a subnetwork according to vertex descriptions we have to consider a pair of vertex subsets. A common technique is to extract from a network an essential subnetwork, the core subgraph of the network. Formal Concept Analysis and closed pattern mining were previously applied to networks with the purpose of reducing extensions of patterns to be core subgraphs. To apply this methodology to two-mode networks, we need to consider the two vertex subsets of two-mode cores and define accordingly abstract closed bi-patterns. Each component of a bi-pattern is then associated to one mode. We also show that the same methodology applies to hub-authority cores of directed networks in which each vertex subset is associated to a role (in or out). We illustrate the methodology both on a two-mode network of epistemological data and on a directed advice network of lawyers.