K-edge Connected Components in Large Graphs: An Empirical Analysis




Sadri, Hanieh

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Graphs play a pivotal role in representing complex relationships across various domains, such as social networks and bioinformatics. Key to many applications is the identification of communities or clusters within these graphs, with k-edge-connected components emerging as an important method for finding well-connected communi- ties. Although there exist other techniques such k-plexes, k-cores, and k-trusses, they are known to have some limitations. This study delves into four existing algorithms designed for computing maximal k-edge-connected subgraphs. We conduct a thorough study of these algorithms to understand the strengths and weaknesses of each algorithm in detail and propose algorithmic refinements to optimize their performance. We provide a careful implementation of each of these algorithms, using which we analyze and compare their performance on graphs of varying sizes. Our work is the first to provide such a direct experimental comparison of these four methods. Finally, we also address an incorrect claim made in the literature about one of these algorithms.



Graph, Community Detection, k-Edge-Connected Components, Clustering, Well-Connected Communities