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# EPC - Edge Percolated Component

#### Definition

For an interaction network G, assign a removing probability p to every edge. Let G' be a realization of the random edge removing from G. If nodes v and w are connected in G', set d

Given a threshold (0 ≤ the threshold ≤ 1), we create 1000 reduced network by asigning a random number between 0 and 1 to every edge and remove edges if their associated random numbers are less than the threshold.

Let the G

_{vw}be 1, otherwise set d_{vw}be 0. The percolated connectivity of v and w, c_{vw}, is defined to be the average of d_{vw}over realizations. The size of percolated component containing node v, s_{v}, is defined to be the sum of c_{vw}over nodes w. The score of node v, EPC(v), is defined to be s_{v}. [LIN, C.-Y. 2008]**cyto-Hubba impelementation:**Given a threshold (0 ≤ the threshold ≤ 1), we create 1000 reduced network by asigning a random number between 0 and 1 to every edge and remove edges if their associated random numbers are less than the threshold.

Let the G

_{k}be the reduced network generated at the*k*th time reduced process. If nodes*u*and*v*are connected in G_{k}, set σ^{k}_{vt}to 1; otherwise σ^{k}_{vt}=0. For a node*v*in G, EPC(*v*) is defined as:#### References

- CHEN, S.-H., CHIN, C.-H., WU, H.-H., HO, C.-W., KO, M.-T. & LIN, C.-Y. cyto-Hubba: A Cytoscape plug-in for hub object analysis in network biology. 20th International Conference on Genome Informatics, 2009.
- CHIN, C.-S. & SAMANTA, M. P. 2003. Global snapshot of a protein interaction network—a percolation based approach. Bioinformatics, 19, 2413-2419.
- LIN, C.-Y., CHIN, C.-H., WU, H.-H., CHEN, S.-H., HO, C.-W. & KO, M.-T. 2008. Hubba: hub objects analyzer—a framework of interactome hubs identification for network biology. Nucleic acids research, 36, W438-W443.