An α-triangle eigenvector centrality of graphs

Centrality is a fundamental concept in complex network analysis, where centrality measures identify important vertices within networks. Over the years, researchers have developed diverse centrality measures from varied perspectives. This paper proposes an α -triangle eigenvector centrality ( α TEC), which is a global centrality measure based on both edge and triangle structures. It can dynamically adjust the influence of edges and triangles through a parameter α ( α ∈ ( 0,1 ] ). The centrality scores for vertices are defined as the eigenvector corresponding to the spectral radius of a nonnegative tensor. By the Perron–Frobenius theorem, α TEC guarantees a unique positive centrality vector for all vertices in connected graphs. Numerical experiments on synthetic and real-world graphs demonstrate that α TEC captures the effects of edges and triangles on vertex importance. As α increases (decreases), the centrality rankings reflect a stronger (weaker) contribution from edge structure and a weaker (stronger) contribution from triangle structure.