Entropic Detection of Chromatic Community Structures
Résumé
The detection of community structure is probably one of the central
trends in complex network emphasizing the complex internal organization
of people, molecules or processes behind social, biological or computer net-
works. . . The issue is to provide a network partition representative of this
organization so that each community presumably gathers nodes sharing a
common mission, purpose or property. Usually the identification is based
on the difference between the connectivity density of the interior and the
boundary of a community. Indeed, nodes sharing a common purpose
or property are expected to interact closely. Although this rule appears
mostly relevant, some fundamental scientific problems like disease module
detection highlight the inability to determine significantly the communi-
ties under this connectivity rule. The main reason is that the connectivity
density is not correlated to a shared property or purpose. Therefore, an-
other paradigm is required for properly formalize this issue in order to
meaningfully detect these communities. In this article we study the com-
munity formation from this new principle. Considering colors formally
figures the shared properties, the issue is thus to maximize group of nodes
with the same color within communities. We study this novel community
framework by introducing new measurement called chromatic entropy as-
sessing the quality of the community structure regarding this constraint.
Next we propose an algorithm solving the community structure detection
based on this new community formation paradigm.