# NC - Network Centrality

#### Definition

The centrality measure, named as NC, calculate a node’s
importance based on the number of edges it connects and
the edges’ clustering coefficients. For a node u, its NC(u)
is defined as the sum of edge clustering coefficients of all
edges directly connected with node u:
where N

NC considers both the centrality of a node and the relationship between it and its neighbors.

The edge clustering coefficient of

_{u}denotes the set of all neighbors of node u. Obviously, NC(u) will be larger if node u has higher degree.NC considers both the centrality of a node and the relationship between it and its neighbors.

**Edge Clustering Coefficient**The edge clustering coefficient of

*E*can be defined as: where_{u,v}*z*denotes the number of triangles that include the edge actually in the network,_{u,v}*d*and_{u}*d*are degrees of node u and node v, respectively. Then, the meaning of_{v}*min(d*is the number of triangles in which the edge E_{u}-1, d_{v}-1)_{u,v}may possibly participate at most.#### References

- WANG, J., LI, M., WANG, H. & PAN, Y. 2012. Identification of essential proteins based on edge clustering coefficient. Computational Biology and Bioinformatics, IEEE/ACM Transactions on, 9, 1070-1080.