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Laplacian CentralityDefinition
If G is a graph of n vertices, then the Laplacian centrality with respect to v is:
where N(v) is the set of neighbors of v in G and d_{G}(v_{i}) is the degree of v_{i} in G.
Laplacian centrality is a simple centrality measure that can be calculated in linear time. It is defined as the drop in the Laplacian energy (i.e. sum of squares of the eigenvalues in the Laplacian matrix) of the graph when the vertex is removed. See: Incremental Laplacian Centrality SoftwareReferences

Hi, Thank you for this great resource pool! I have a question regarding the laplacian centrality measure. In the R package centiserve it seems to compute laplacian centrality only for unweighted graphs. Do you perhaps know how I can compute laplacian centrlaity and the total graph energy for directed and weighted graphs? Yingjie 

Add Replay  written October 23, 2018, 2:11 pm by Yingjie 