Social centrality using network hierarchy and community structure


Several centrality measures have been formulated to quantify the notion of ‘importance’ of actors in social networks. Current measures scrutinize either local or global connectivity of the nodes and have been found to be inadequate for social networks. Ignoring hierarchy and community structure, which are inherent in all human social networks, is the primary cause of this inadequacy. Positional hierarchy and embeddedness of an actor in the community are intuitively crucial determinants of his importance. The theory of social capital asserts that an actor’s importance is derived from his position in network hierarchy as well as from the potential to mobilize resources through intra-community (bonding) and inter-community (bridging) ties. Inspired by this idea, we propose a novel centrality measure social centrality (SC) for actors in social networks. Our measure accounts for—(1) an individual’s propensity to socialize, and (2) his connections within and outside the community. These two factors are suitably aggregated to produce social centrality score. Comparative analysis of SC measure with classical and recent centrality measures using large public networks shows that it consistently produces more realistic ranking of nodes. The inference is based on the available ground truth for each tested networks. Extensive analysis of rankings delivered by SC measure and mapping with known facts in well-studied networks justifies its effectiveness in diverse social networks. Scalability evaluation of SC measure justifies its efficacy for real-world large networks.

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    We experimented with various community detection algorithms available in the Python igraph library, and chose the Multilevel algorithm because it was the fastest.

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    Weighted versions of classical centrality measures were used from the Python igraph library; Python code for implemented measures and datasets used for experimentation are available at

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    STC ran out of memory and SoCap did not complete even after running for a day.

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    Enron employee position in organization structure obtained from

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    Synthetic networks generated using igraph package; ER: (n, m \(=\) 2n); WS: (n, dim \(=\) 1, nei \(=\) 4, \(p=0.3\)); FF:, ambs \(=\) 4, bw.factor \(=\) 0.2, fw.prob \(=\) 0.3)

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    Real-world networks downloaded from


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Correspondence to Rakhi Saxena.

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Saxena, R., Kaur, S. & Bhatnagar, V. Social centrality using network hierarchy and community structure. Data Min Knowl Disc 32, 1421–1443 (2018).

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  • Centrality
  • Social capital
  • Hierarchy
  • Community
  • Strength of ties
  • k-Truss decomposition