Hypernode Graphs for Learning from Binary Relations between Groups in Networks

International audienceThe aim of this paper is to propose methods for learning from interactions between groups in networks. We introduced hypernode graphs in Ricatte et al (2014) a formal model able to represent group interactions and able to infer individual properties as well. Spectral graph learning algorithms were extended to the case of hypern-ode graphs. As a proof-of-concept, we have shown how to model multiple players games with hypernode graphs and that spectral learning algorithms over hyper-node graphs obtain competitive results with skill ratings specialized algorithms. In this paper, we explore theoretical issues for hypernode graphs. We show that hypernode graph kernels strictly generalize over graph kernels and hypergraph kernels. We show that hypernode graphs correspond to signed graphs such that the matrix D − W is positive semidefinite. It should be noted that homophilic relations between groups may lead to non homophilic relations between individ-uals. Moreover, we also present some issues concerning random walks and the resistance distance for hypernode graphs