Modularity-based Network Decomposition

Synonyms

Network modularity

Definition

In the study of biological networks, modularity is mainly used to describe the degree to which a network may be separated into somehow structurally and functionally independent modules. A quantitative measure of the modularity of a complex network was introduced by Newman and Girvan (2004) (Eq. 1).

$$ Q = \sum\limits_i {({e_{{ii}}} - a_i^2)} = \sum\limits_i {\left[ {\frac{{{l_i}}}{L} - {{\left(\frac{{{d_i}}}{{2L}}\right)}^2}} \right]} $$

(1)

where e _ii is the fraction of links between nodes in module i, calculated as the number of links (l _i ) in the module divided by the total number of links (L) in the network, a _i is an item showing the effect of intra-module connectivity which is calculated as the sum of degrees of the nodes in module i (d _i ) normalized by the sum of degrees in the whole network (which equals to twice the number of the links). Different partitions of a network have different modularity values. Therefore, modularity can be...