# Daniella Zhou: The Statistical Study of Clique-based Community Detection for Empirical Networks

**Time: **
Wed 2022-09-07 09.00 - 09.40

**Location: **
Albano house 1, floor 3, Room T (Cramér)

**Respondent: **
Daniella Zhou

**Supervisor: **
Chun-Biu Li

**Abstract:**

The Clique Percolation Method (CPM) is a community detection method that allows the presence of overlapping communities due to its local topological properties. The core of the method is the so-called k-clique, defined as a complete subgraph with k nodes. A community is defined as a set of nodes that belong to a series of adjacent k-cliques. This study is focused on the weighted Clique Percolation Method (CPMw) and its performance in synthetic and real-world datasets. Two crucial parameters of the CPMw are the number of nodes in the clique, k, and the clique intensity, I. The intensity parameter can be thought of as scissors that cut the connections between nodes in a network and has a significant impact on the outcome. The best combination of k and I is the one that allows the CPMw to identify weighted communities with the strongest intra-connections, while keeping the inter- connections of communities as loose as possible. The CPMw is restricted to 3-cliques and is conducted on the k-nearest neighbor graphs of an evenly distributed synthetic dataset and an unevenly distributed real-world dataset. The results are evaluated with a fuzzy clustering validation index, PCAES, and the optimal result is selected at the maximum PCAES. Based on the results, we can conclude that the CPMw performs prominently when networks have communities of even sparsity. Well-structured communities with overlaps are detected. However, unexpected small-sized noisy communities occur in a region with high local intensity.

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