Exchange-based diffusion in Hb-Graphs

Abstract

AbstractHighlighting important information of a network is commonly achieved by using random walks related to diffusion over such structures. Complex networks, where entities can have multiple relationships, call for a modeling based on hypergraphs. But, the limitation of hypergraphs to binary entities in co-occurrences has led us to introduce a new mathematical structure called hyperbaggraphs, that relies on multisets. This is not only a shift in the designation but a real change of mathematical structure, with a new underlying algebra. Diffusion processes commonly start with a stroke at one vertex and diffuse over the network. In the original conference article—(Ouvrard et al. 2018)—that this article extends we have proposed a two-phase step exchange-based diffusion scheme, in the continuum of spectral network analysis approaches, that takes into account the multiplicities of entities. This diffusion scheme allows to highlight information not only at the level of the vertices but also at the regrouping level. In this paper, we present new contributions: the proofs of conservation and convergence of the extracted sequences of the diffusion process, as well as the illustration of the speed of convergence and comparison between classical and modified random walks; the algorithms of the exchange-based diffusion and the modified random walk; the application to two use cases, one based on Arxiv publications and another based on Coco dataset images. All the figures have been revisited in this extended version to take the new developments into account.