Table 1

Different Definitions of module in protein interaction network[29-31,39,40]

Module Definitions


Module Names

Computational Formula


Strong Module

In a strong module each vertex has more connections within the module than with the rest of the graph.


Weak Module

In a weak module the sum of all degrees within subgraph H is larger than the sum of all degrees toward the rest of the network.


Chen et al.

A combination of weak module and a new less stringent condition, which is that, collectively, the in-degrees of the vertices in the subgraph are significantly greater than the out-degrees.


Luo et al.

A subgraph H ⊂ G is a module if its modularity MH >1. In the definition, ind(H) denotes the number of edges within H and outd(H) denotes the number of edges that connect H to the remaining part of G.



λ-module is a general version of weak module. When λ=1, it would be the same as weak module defined by Radicchi et al. By changing the values of parameter λ, one can get different modules in the protein interaction networks.



λ*-module is a more general version of λ-module, which is used for weighted protein interaction networks.


In Table 1, different criterions are shown that the given subgraph HG is a module.

denotes the “in-degree” of vertex i (i.e. the number of edges connecting vertex i to other vertices belonging to H) and denotes the “out-degree” of vertex i (ie. the number of edges connecting vertex i and other vertices in the rest of the graph G). Let ki be the degree of vertex i. Then, . and are the weighted “in-degree” and “out-degree” of vertex i, respectively.

Wang et al. BMC Genomics 2010 11(Suppl 3):S10   doi:10.1186/1471-2164-11-S3-S10

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