Modularity

Modularity is the degree to which a system's components may be separated and recombined. The meaning of the word, however, can vary somewhat by context:

Modularity (biology)

Modularity refers to the ability of a system to organize discrete, individual units that can overall increase the efficiency of network activity and, in a biological sense, facilitates selective forces upon the network. It has been observed in all model systems and can be studied at nearly every scale of organization (molecular interactions all the way up to the whole organism).

Evolution of Modularity

The exact evolutionary origins of biological modularity has been debated for over the past decade. In the mid 90’s, Günter Wagner argued that modularity could have arisen and been maintained through the complex interaction of four potential evolutionary modes of action:

[1] Selection for the rate of adaptation: If different complexes evolve at different rates, than those evolving more quickly reach fixation in a population faster than other complexes. Thus, common evolutionary rates could be canalizing certain proteins to evolve together while preventing other genes from being co-opted unless there is a shift in evolutionary rate.

Modularity (networks)

Modularity is one measure of the structure of networks or graphs. It was designed to measure the strength of division of a network into modules (also called groups, clusters or communities). Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Modularity is often used in optimization methods for detecting community structure in networks. However, it has been shown that modularity suffers a resolution limit and, therefore, it is unable to detect small communities. Biological networks, including animal brains, exhibit a high degree of modularity.

Motivation

Many scientifically important problems can be represented and empirically studied using networks. For example, biological and social patterns, the World Wide Web, metabolic networks, food webs, neural networks and pathological networks are real world problems that can be mathematically represented and topologically studied to reveal some unexpected structural features. Most of these networks possess a certain community structure that has substantial importance in building an understanding regarding the dynamics of the network. For instance, a closely connected social community will imply a faster rate of transmission of information or rumor among them than a loosely connected community. Thus, if a network is represented by a number of individual nodes connected by links which signify a certain degree of interaction between the nodes, communities are defined as groups of densely interconnected nodes that are only sparsely connected with the rest of the network. Hence, it may be imperative to identify the communities in networks since the communities may have quite different properties such as node degree, clustering coefficient, betweenness, centrality. etc., from that of the average network. Modularity is one such measure, which when maximized, leads to the appearance of communities in a given network.