Exponential quality function for community detection in complex networks

Abstract

One of the most popular topics in analyzing complex networks is the detection of its community structure. In this paper, we introduce a new criterion for community detection, called the E‐quality function. The quality of an individual community is defined as a difference between its benefit and its cost, where both are exponential functions of the number of internal edges and the number of external edges, respectively. The obtained optimization problem, maximization of the E‐quality function over all possible partitions of a network, is solved by the variable neighborhood search (VNS)‐based heuristic. Comparison of the new criterion and modularity is performed on the usual test instances from the literature. Experimental results obtained both on artificial and real networks show that the proposed E‐quality function allows detection of the communities existing in the network.

Some properties of e-quality function for network clustering

“…We considered different classes of artificial networks introduced in [7] and analyzed whether E-quality function tends to merge or split clusters that are unambiguously defined. Our theoretical results confirmed experimental results presented in [6], and showed that E-quality function detects expected and reasonable clusters, which is not the case with the Modularity function.…”

“…In this subsection we briefly present the necessary notation introduced in [6]. Let G = (V, E) be a simple graph defined by a set V of n vertices (nodes) and a set E of m edges that connect pairs of vertices.…”

“…Fortunato et al [7] found, through several examples on artificial networks, that optimizing modularity in large networks can fail to resolve small clusters even in cases where clusters are unambiguously defined. In the literature, this problem is broadly addressed as the resolution limit problem, and it initiated research for a new quality function that focuses on a local definition of claster rather than definitions relying on a global null model [4,9,6].…”

“…In this paper, we focus on theoretical analysis of Exponential Quality function (E-quality) for network clustering, proposed in [6]. We considered different classes of artificial networks introduced in [7] and analyzed whether E-quality function tends to merge or split clusters that are unambiguously defined.…”

Space-Time Evolution of Subway Vulnerability Based on Hypergraph Space

“…Džamić et al introduced a new community structure detection standard for complex networks. is new detection standard provides a new path for community detection [9]. Latora and Marchiori proposed a complicated subway network model based on transportation efficiency [10].…”