Detect overlapping and hierarchical community structure in networks

Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two properties of community structure separately. This paper proposes an algorithm (EAGLE) to detect both the overlapping and hierarchical properties of complex community structure together. This algorithm deals with the set of maximal cliques and adopts an agglomerative framework. The quality function of modularity is extended to evaluate the goodness of a cover. The examples of application to real world networks give excellent results.

💡 Research Summary

The paper addresses a fundamental limitation in community detection for complex networks: most existing methods either produce a hard partition (each node belongs to exactly one community) or detect overlapping communities without revealing any hierarchical organization. Real‑world networks, however, often exhibit both overlapping and hierarchical structures simultaneously. To fill this gap the authors propose EAGLE (Agglomerative Hierarchical Clustering based on Maximal Clique), an algorithm that works directly on the set of maximal cliques of a graph and merges them in a similarity‑driven agglomerative fashion.

Algorithmic framework

1. Maximal‑clique extraction – All maximal cliques are enumerated (the authors use the Bron–Kerbosch algorithm). Cliques smaller than a user‑defined size threshold k (typically 3–6) and “subordinate” cliques that are subsets of larger ones are discarded. The remaining cliques become the initial communities; isolated vertices that belong to no retained clique are treated as singleton communities.
2. Similarity measure – For any two communities C₁ and C₂ the similarity M is defined as

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