Table 4 Formal Representation of Graph Measures.
From: Computational characterization and identification of human polycystic ovary syndrome genes
Name | Function | Descriptions |
|---|---|---|
Degree | \({{\rm{K}}}_{{\rm{i}}}^{1}\) | the number of direct interaction partners of node i |
Degree-2 | \({{\rm{K}}}_{{\rm{i}}}^{2}\) | the number of 2-step interaction partners of node i |
1st PCOS ratio | \({{\rm{K}}}_{{\rm{i}}}^{1,{\rm{P}}}/{{\rm{K}}}_{{\rm{i}}}^{1}\) | \({{\rm{K}}}_{{\rm{i}}}^{1,{\rm{P}}}\) is the number of direct interactions between node i and proteins encoded by PCOS genes |
2nd PCOS ratio | \({{\rm{K}}}_{{\rm{i}}}^{2,{\rm{P}}}/{{\rm{K}}}_{{\rm{i}}}^{2}\) | \({{\rm{K}}}_{{\rm{i}}}^{2,{\rm{P}}}\) is the number of 2-step interaction between node i and proteins encoded by PCOS genes |
Betweenness | \(\sum _{\begin{array}{c}j\in V,k\in V\\ j\ne i,k\ne i\end{array}}\frac{\sigma (j,i,k)}{\sigma (j,k)}\) | \(\sigma (j,I,k)\) is the total number of shortest connections between nodes j and k, where each shortest connection has to pass node i, and \(\sigma (j,k)\) is the total number of shortest connections between j and k. The set V of nodes represents all proteins in the network. |
K-core | K | A K-core of a graph can be obtained by recursively removing all nodes with a degree less than K, until all nodes in the remaining graph have a degree at least K. |
