Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more. Modularity is a quality function that measures the difference between the number of edges found within clusters minus the number of edges one would statistically ex...

We examine hierarchical modularity modularity on multiple levels, in which the modules at a lower level of abstraction can serve as nodes in a network at a higher level of abstraction that also has positive modularity as well as degree of modularity on a single level of abstraction, in evolved neural networks in single-task, parallel-subtask environments, and sequential-subtask environments, us...

Introduction In the second half of the last century, modularity emerged as a powerful idea for dealing with increasingly complex systems (Schilling 2000; Simon 1962). Noting the transformative power of this perspective, Baldwin and Clark (1997) declared the arrival of the “age of modularity.” They argue that modularity was at the heart of the remarkable rate of innovation in recent history, sin...

Modularity is widely used to effectively measure the strength of the community structure found by community detection algorithms. However, modularity maximization suffers from two opposite yet coexisting problems: in some cases, it tends to favor small communities over large ones while in others, large communities over small ones. The latter tendency is known in the literature as the resolution...

Bipartite networks are an important category of complex networks in human social activities. Newman and Girvan proposed a measurement called modularity to evaluate community structure in unipartite networks called modularity. Due to the success of modularity in unipartite networks, bipartite modularity is developed according to different understandings of community in bipartite networks which a...

Expressions and bounds for Newman's modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and the hop count of the shortest paths vary when the as...