Modularity and anti-modularity in networks with arbitrary degree distribution
Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the duplication or fusion of nodes. While each of these mechanisms can have a different cause depending on whether the network is biological, technological, or social, their impact on the network's structure, as well as its local and global properties, is similar. This allows us to study how each of these mechanisms affects networks either alone or together with the other processes, and how they shape the characteristics that have been observed. We study how a network's growth parameters impact the distribution of edges in the network, how they affect a network's modularity, and point out that some parameters will give rise to networks that have the opposite tendency, namely to display anti-modularity. Within the model we are describing, we can search the space of possible networks for parameter sets that generate networks that are very similar to well-known and well-studied examples, such as the brain of a worm, and the network of interactions of the proteins in baker's yeast.