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 real-world 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 industry-oriented corporate network of Germany.
The first author is supported by funding from the European Research Council (ERC) under the EU Horizon 2020 research and innovation programme (grant agreement 638946). Thanks to the CORPNET group (http://corpnet.uva.nl) for useful suggestions.
- 1.Adams, M.: Cross holdings in Germany. J. Inst. Theor. Econ. 155(1), 80–109 (1999)Google Scholar
- 3.Barabási, A.L.: Network Science. Cambridge University Press (2016)Google Scholar
- 4.Battiston, F., Nicosia, V., Chavez, M., Latora, V.: Multilayer motif analysis of brain networks. Chaos Interdiscip. J. Nonlinear Sci. 27(4), article 047,404 (2017)Google Scholar
- 8.Dickison, M.E., Magnani, M., Rossi, L.: Multilayer Social Networks. Cambridge University Press (2016)Google Scholar
- 11.Garcia-Bernardo, J., Takes, F.W.: The effects of data quality on the analysis of corporate board interlock networks (2017). arXiv: 1612.01510
- 12.Ghazizadeh, S., Chawathe, S.S.: SEuS: Structure extraction using summaries. In: Proceedings of the International Conference on Discovery Science, pp. 71–85 (2002)Google Scholar
- 13.Haiyan, H., Xifeng, Y., Jiawei, H., Jasmine, Z.X.: Mining coherent dense subgraphs across massive biological networks for functional discovery. Bioinformatics 21(1), 213–221 (2005)Google Scholar
- 21.Ribeiro, P., Silva, F.: G-tries: An efficient data structure for discovering network motifs. In: Proceedings of the ACM Symposium on Applied Computing, pp. 1559–1566 (2010)Google Scholar
- 22.Saeed, S., Saeed, J.: Fast parallel all-subgraph enumeration using multicore machines. Sci. Program. 2015, 901,321 (2015)Google Scholar
- 23.Solé-Ribalta, A., De Domenico, M., Arenas, A.: Centrality rankings in multiplex networks. In: Proceedings of the International Conference on Web Science, pp. 149–155 (2014)Google Scholar
- 25.Vitali, S., Glattfelder, J.B., Battiston, S.: The network of global corporate control. PloS one 6(10), e25,995 (2011)Google Scholar
- 26.Wernicke, S.: A faster algorithm for detecting network motifs. In: Proceedings of the Workshop on Algorithms in Bioinformatics, pp. 165–177 (2005)Google Scholar