|Common characters of complex networks|
|Scale-free||It is a most notable characteristic in complex systems. It was used to desibe the finding that most nodes in a network have few neighbors while few nodes have large amount of neighbors. In most cases, the connectivity distribution asymptotically follows a power law . It can be expressed in , where P(k) is the number of nodes with k degrees, k is connectivity/degrees and γ is a constant.|
|Small-world||It is a terminology in network analyses to depict the average distance between nodes in a network is short, usually logarithmically with the total number of nodes . It means the network nodes are always closely related with each other.|
|Modularity||It was used to demonstrate a network which could be naturally divided into communities or modules . Each module in gene regulation networks is considered as a functional unit which consisted of several elementary genes and performed an identifiable task [23,46]. A modularity value can be calculated by Newman’s method  which was used to measure how well a network is able to be separated into modules. The value is between 0 to 1.|
|Hierarchy||It was used to depict the networks which could be arranged into a hierarchy of groups representing in a tree structure. Several studies demonstrated that metabolic networks are usually accompanied by a hierarchical modularity [37,44]. It was potentially consistent with the notion that the accumulation of many local changes affects the small highly integrated modules more than the larger, less integrated modules . One of the most important signatures for hierarchical modular organizations is that the scaling of clustering coefficient follows C(k) ~ k−γ (scaling law), in which k is connectivity and γ is a constant .|
Deng et al.
Deng et al. BMC Bioinformatics 2012 13:113 doi:10.1186/1471-2105-13-113