2021/05/13 by Tanguy Fardet, Anna Levina, Fardet, Tanguy +1 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Clustering Algorithms Research #Complex Network Analysis Techniques #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2105.06318
openalex publication_date 2021/05/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Weights and directionality of the edges carry a large part of the information\nwe can extract from a complex network. However, many network measures were\nformulated initially for undirected binary networks. The necessity to\nincorporate information about the weights led to the conception of the multiple\nextensions, particularly for definitions of the local clustering coefficient\ndiscussed here. We uncover that not all of these extensions are fully-weighted;\nsome depend on the degree and thus change a lot when an infinitely small weight\nedge is exchanged for the absence of an edge, a feature that is not always\ndesirable. We call these methods ``hybrid'' and argue that, in many situations,\none should prefer fully-weighted definitions. After listing the necessary\nrequirements for a method to analyze many various weighted networks properly,\nwe propose a fully-weighted continuous clustering coefficient that satisfies\nall the previously proposed criteria while also being continuous with respect\nto vanishing weights. We demonstrate that the behavior and meaning of the\nZhang--Horvath clustering and our new continuous definition provide\ncomplementary results and significantly outperform other definitions in\nmultiple relevant conditions. Using synthetic and real-world examples, we show\nthat when the network is inferred, noisy, or very heterogeneous, it is\nessential to use the fully-weighted clustering definitions.\n