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Table 1 Different Definitions of module in protein interaction network[2931, 39, 40]

From: Recent advances in clustering methods for protein interaction networks

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 in-degrees of the vertices in the subgraph are significantly greater than the out-degrees.

[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]

λ-module

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.

[39]

λ*-module

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

[40]

  1. In Table 1, different criterions are shown that the given subgraph H G is a module.
  2. 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 k i be the degree of vertex i. Then, . and are the weighted “in-degree” and “out-degree” of vertex i, respectively.