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 Nu 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 Eu,v can be defined as:
where zu,v denotes the number of triangles that include the
edge actually in the network, du and dv are degrees of node
u and node v, respectively. Then, the meaning of min(du-1, dv-1) is the number of triangles in which the edge Eu,v
may possibly participate at most.
NC considers both the centrality of a node and the relationship between it and its neighbors.
Edge Clustering Coefficient
The edge clustering coefficient of Eu,v can be defined as:
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.