Table 1 

Different Definitions of module in protein interaction network[2931,39,40] 

Module Definitions 
References 



Module Names 
Computational Formula 
Descriptions 



Strong Module 
In a strong module each vertex has more connections within the module than with the rest of the graph. 
[29] 



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. 
[29] 



Chen et al. 
A combination of weak module and a new less stringent condition, which is that, collectively, the indegrees of the vertices in the subgraph are significantly greater than the outdegrees. 
[30] 



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. 
[31] 



λmodule 
λmodule 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. 
[39] 



λ*module 
λ*module is a more general version of λmodule, which is used for weighted protein interaction networks. 
[40] 



In Table 1, different criterions are shown that the given subgraph H ⊂ G is a module. denotes the “indegree” of vertex i (i.e. the number of edges connecting vertex i to other vertices belonging to H) and denotes the “outdegree” of vertex i (ie. the number of edges connecting vertex i and other vertices in the rest of the graph G). Let k_{i} be the degree of vertex i. Then, . and are the weighted “indegree” and “outdegree” of vertex i, respectively. 

Wang et al. BMC Genomics 2010 11(Suppl 3):S10 doi:10.1186/1471216411S3S10 