Exchange-Based Diffusion in Hb-Graphs: Highlighting Complex Relationships
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Most networks tend to show complex and multiple relationships between entities. Networks are usually modeled by graphs or hypergraphs; nonetheless a given entity can occur many times in a relationship: this brings the need to deal with multisets instead of sets or simple edges. Diffusion processes are useful to highlight interesting parts of a network: they usually start with a stroke at one vertex and diffuse throughout the network to reach a uniform distribution. Several iterations of the process are required prior to reaching a stable solution. We propose an alternative solution to highlighting main components of a network using a diffusion process based on exchanges; it is an iterative two-phase step exchange process. This process allows to evaluate the importance not only at the vertices level but also at the regrouping level. To model the diffusion process, we extend the concept of hypergraphs that are family of sets to family of multisets, that we call hb-graphs.
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