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arXiv · 2408.07627

Clique structure and other network properties of the tensor product of Erd\H{o}s-R\'enyi graphs

Umit Islak·Bugra Incekara
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Abstract

We analyze the number of cliques of given size and the size of the largest clique in tensor product $G \times H$ of two Erd\H{o}s-R\'enyi graphs $G$ and $H$. Then an extended clustering coefficient is introduced and is studied for $G \times H$. Restriction to the standard clustering coefficient has a direct relation to the local efficiency of the graph, and the results are also interpreted in terms of the efficiency. As a last statistic of interest, the number of isolated vertices is analyzed for $G \times H$. The paper is concluded with a discussion of the modular product of random graphs, and the relation to the maximum common subgraph problem.

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Umit Islak, Bugra Incekara. 2024-08-14. Clique structure and other network properties of the tensor product of Erd\H{o}s-R\'enyi graphs. https://arxiv.org/abs/2408.07627

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