Influential nodes in ray cluster hypergraph networks

Vivek Dubey

doi:10.1016/j.eswa.2025.127014

Influential nodes in ray cluster hypergraph networks

2025-02-01

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DOI：10.1016/j.eswa.2025.127014

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Graphs and hypergraphs are used to represent different types of networks. We observe that a few important network types cannot be appropriately represented by existing graph or hypergraph techniques, such as dynamic directed networks where sources or sinks may/ may not exist for a flow at a certain time. In those cases, the edges /hyperedges are not enough to represent the flow containing only sources or sinks. Ray graphs are introduced to capture this particular notion. On the other hand, cluster hypergraphs have cluster nodes that contain simple nodes. In reality, groups of people exist, and the groups may act as a single body while the internal members display some complex relationships. Thus, any type of complex social network where group nodes exist could be represented by cluster hypergraphs accurately. We define ray (bi-weighted) cluster hypergraphs and related notions to address these issues and to further generalize graphs, develop and present corresponding theories of complete cluster hypergraphs, ray (bi-weighted) cluster hypergraphs, and uniform cluster hypergraphs. Influence measurement is an urgent research area. The measures of influence in the literature do not capture group or hyperedge influences. This article discusses a new measure of influence for nodes in social networks based on ray cluster hypergraph theory. We illustrate the concepts through data on projects (research papers) represented by hyperedges and contributors to the projects (authors) represented through clusters in the ray cluster hypergraphs conveniently, and then the importance of the influence of nodes is discussed. The significance of hypergraphs in networks has been well-established in various domains, including evolutionary dynamics, vector centrality, synchronization, and higher-order interactions. This study adds to these foundational works to propose a novel approach for measuring influence in complex networks.

Keywords:

Ray graphs

Bi-weighted graphs

Cluster nodes

Bi-weighted cluster hypergraphs

Influential nodes

Complex networks

Influential nodes in ray cluster hypergraph networks

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