# SoECC - Sum of Edge Clustering Coefficient

#### Definition

SoECC define the sum of edge clustering coefficients of node u as:
where N

SoECC is a method for identifying essential proteins based on edge clustering coefficient which binds characteristics of edges and nodes effectively.

For an edge E

_{u}denotes the set of all neighbor nodes of node u. Obviously, SoECC(u) will be larger if node u that with higher degree. In this sense, SoECC has a integrated characteristic of edges and nodes.SoECC is a method for identifying essential proteins based on edge clustering coefficient which binds characteristics of edges and nodes effectively.

**Edge Clustering Coefficient**For an edge E

_{u,v}connecting node u and node v, we pay attention to how many other nodes that adjoin both u and v. The edge clustering coefficient of E_{u,v}can be defined by the following expression: where z_{u,v}denotes the number of triangles that include the edge actually in the network, d_{u}and d_{v}are degrees of node u and node v, respectively. Then the meaning of min(d_{u}−1, d_{v}−1) is the number of triangles in which the edge E_{u,v}may possibly participate at most.#### Requirements

Unweighted, undirected network.

#### Software

#### References

- WANG, H., LI, M., WANG, J. & PAN, Y. 2011. A New Method for Identifying Essential Proteins Based on Edge Clustering Coefficient. In: CHEN, J., WANG, J. & ZELIKOVSKY, A. (eds.) Bioinformatics Research and Applications. Springer Berlin Heidelberg. DOI: 10.1007/978-3-642-21260-4_12