For a node \(v\) in G, \(EPC(v)\) is defined as: $$EPC(v)=\frac{1}{\left|v\right|}\sum_{k=1}^{1000}\sum_{t\in e}\delta_{vt}^{k}$$ Given a threshold \((0 \leq the threshold \leq 1)\), 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 \(\delta_{vt}^{k}\) to 1; otherwise \(\delta_{vt}^{k}=0\).
epc(graph, vids = V(graph), threshold = 0.5)The input graph as igraph object
Vertex sequence, the vertices for which the centrality values are returned. Default is all vertices.
The threshold parameter, for filter graph and create reduced one, which must be between 0 and 1. The default is 0.5.
A numeric vector contaning the centrality scores for the selected vertices.
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 \(d_{vw}\) 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 \(s_{v}\). More detail at EPC-Edge Percolated Component
Lin, Chung-Yen, et al. "Hubba: hub objects analyzer-a framework of interactome hubs identification for network biology." Nucleic acids research 36.suppl 2 (2008): W438-W443.
Chen, Shu-Hwa, et al. "cyto-Hubba: A Cytoscape plug-in for hub object analysis in network biology." 20th International Conference on Genome Informatics. 2009.
# NOT RUN {
g <- graph(c(1,2,2,3,3,4,4,2))
epc(g)
# }
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