Detecting Motifs in Multiplex Corporate Networks.

The main topic of this paper is the discovery of motifs in multiplex corporate networks. Network motifs are small subgraphs occurring at significantly higher numbers than in similar random networks. They can be seen as the building blocks of a complex network. In realworld network data, multiple types of (possibly overlapping) relationships may be present among the nodes, forming so-called multiplex networks. Detecting motifs in such networks is difficult, as existing subgraph enumeration algorithms are not directly applicable to multiplex network data. In addition, the selection of a proper multiplex null model to test the significance of the enumerated subgraphs is nontrivial. This paper addresses these two problems, resulting in three contributions. First, we present a method based on layer encoding for adequately handling the multiplex aspect in subgraph enumeration. Second, a null model is proposed that is able to preserve the relationship between the different types of links, taking into account that a particular link type may be the result of a projection from a bipartite network. Finally, we perform experiments on corporate network data from Germany, in which around 75 000 nodes represent corporations and roughly 195 000 links represent connectedness of firms based on shared board members and ownership. We demonstrate how incorporating the multiplex aspect in motif detection is able to reveal new insights that could not be obtained by studying only one type of relationship. Furthermore, results uncover how the financial sector is over-represented in the more complex motifs, hinting at a surprisingly prominent role of the financial sector in the largely industryoriented corporate network of Germany.