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arXiv · 2108.10458

Supernodes

Su Yuan Chan·Kerri Morgan·Nick Parsons·Julien Ugon
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Abstract

In this paper, we present two new concepts related to subgraph counting where the focus is not on the number of subgraphs that are isomorphic to some fixed graph $H$, but on the frequency with which a vertex or an edge belongs to such subgraphs. In particular, we are interested in the case where $H$ is a complete graph. These new concepts are termed vertex participation and edge participation respectively. We combine these concepts with that of the rich-club to identify what we call a Super rich-club and rich edge-club. We show that the concept of vertex participation is a generalisation of the rich-club. We present experimental results on randomised Erd\"{o}s R\'{e}nyi and Watts-Strogatz small-world networks. We further demonstrate both concepts on a complex brain network and compare our results to the rich-club of the brain.

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Su Yuan Chan, Kerri Morgan, Nick Parsons, Julien Ugon. 2021-08-24. Supernodes. https://arxiv.org/abs/2108.10458

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