Entropic detection of chromatic community structures

Abstract The identification of community structure represents a central challenge in the field of complex networks. The objective is to ascertain the internal organization of agents within a network and to provide a representative network partition. Each community is presumed to comprise nodes sharing a common objective or property. The identification of these communities is typically based on the difference in connectivity density between the interior and border of a community. Indeed, nodes sharing a common purpose or property are expected to interact closely. Although this rule appears to be relevant, it nevertheless fails to address fundamental scientific problems such as disease module detection, thereby highlighting the inability to meaningfully determine communities based solely on connectivity for this situation. Consequently, another paradigm is necessary to formalize this problem accurately and detect these communities objectively. In this article, we propose a new framework to study this novel community formation property. Considering that colors represent shared properties, the problem is to maximize groups of nodes of the same color within communities. We propose a novel algorithm for detecting community structure based on a new measurement, chromatic entropy, which quantitatively assesses the community structure based on color constraint.