# Community Centrality

#### Definition

**(I)**

[NEWMAN, M. E. J. 2006]

**(II)**

For node i the community centrality is: where the main sum is over the N communities to which node i belongs, and S(j,k) refers to the similarity between community j and k, calculated as the Jaccard coefficient for the number of shared nodes between each community pair, and this is averaged over the m communities paired with community j and in which node i jointly belongs.

[KALINKA, A. T. 2011]

**(III)**

Community centrality of a given edge (or node) was defined as the sum of local influence zones of all network edges (or nodes) including the given edge. Thus community centrality represents an integrated measure of the whole network’s influence to one of its edges or nodes.

It is worth to note that the community centrality measure we use is not the same community centrality measure introduced by Mark Newman [2006]. The two community centralities are similar in the sense that they take into account the mesoscopic (modular) structure of the network to define the centrality value. However, the Newman-type community centrality is derived from eigenvector analysis, while ours represents the sum of local influence zones of all nodes or edges on each node or edge.

[SZALAY-BEKŐ, M., 2012]

#### Software

#### References

- KALINKA, A. T. & TOMANCAK, P. 2011. linkcomm: an R package for the generation, visualization, and analysis of link communities in networks of arbitrary size and type. Bioinformatics, 27, 2011-2. PMID: 21596792 DOI: 10.1093/bioinformatics/btr311
- KOVÁCS, I. A., PALOTAI, R., SZALAY, M. S. & CSERMELY, P. 2010. Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy, Identify Key Nodes and Predict Network Dynamics. PLoS ONE, 5, e12528. DOI: 10.1371/journal.pone.0012528
- NEWMAN, M. E. J. 2006. Finding community structure in networks using the eigenvectors of matrices. Physical Review E, 74, 036104. DOI: 10.1103/PhysRevE.74.036104
- SZALAY-BEKŐ, M., PALOTAI, R., SZAPPANOS, B., KOVÁCS, I. A., PAPP, B. & CSERMELY, P. 2012. ModuLand plug-in for Cytoscape: determination of hierarchical layers of overlapping network modules and community centrality. Bioinformatics, 28, 2202-2204.