Grant: Alliance Grants

Hypergraphs have recently emerged as a useful representation for complex networks since they allow capturing more general relations than graphs. Research on the generalization of various graph-based tools and techniques is booming and, in parallel, new software packages are being developed. Having said that, the theory and tools are still not sufficiently developed to allow most problems to be tackled directly within this context. Hypergraphs are of particular interest in the field of knowledge discovery where most problems currently modelled as graphs would be more accurately modelled as hypergraphs. Those in the knowledge discovery field are particularly interested in the generalization of the concepts of modularity and diffusion to hypergraphs. Such generalizations require a firm theoretical base on which to develop these concepts. Unfortunately, although hypergraphs were formally defined in the 1960s (and various realizations of hypergraphs were studied long before that), the general formal theory is not as mature as required for the applications of interest to practitioners. The main goal of this collaboration is to develop formal theory, in conjunction with development of concrete applications. Given that different research groups in various parts of the world have recently started pursuing results in this direction, the proposal seems particularly well-timed as an occasion for the cross-pollination of research directions, the establishment of new collaborations and the exchange of tools and techniques.