κ-Path Centrality
Definition
κ-path edge centrality
For each edge e of a graph G = (V,E), the κ-path edge centrality Lκ(e) of e is defined as the sum, over all possible source nodes s, of the frequency with which a message originated from s traverses e, assuming that the message traversals are only along random simple paths of at most κ edges.
where s are all the possible source nodes, σκs(e) is the number of
κ-paths originating from s and traversing the edge e and, finally, σκs is the number of κ-paths originating from s.
In practical cases, the above Eq. for κ-path edge centrality can not be feasible because it requires to count all the κ-paths originating from all the source nodes s and such a number can be exponential in the number of nodes of G. To this purpose, we need to design some algorithms capable of efficiently approximating the value of κ-path edge centrality.
See K-Path Centrality See Geodesic K-Path Centrality
For each edge e of a graph G = (V,E), the κ-path edge centrality Lκ(e) of e is defined as the sum, over all possible source nodes s, of the frequency with which a message originated from s traverses e, assuming that the message traversals are only along random simple paths of at most κ edges.
In practical cases, the above Eq. for κ-path edge centrality can not be feasible because it requires to count all the κ-paths originating from all the source nodes s and such a number can be exponential in the number of nodes of G. To this purpose, we need to design some algorithms capable of efficiently approximating the value of κ-path edge centrality.
See K-Path Centrality See Geodesic K-Path Centrality
Software
References
- DE MEO, P., FERRARA, E., FIUMARA, G. & RICCIARDELLO, A. 2012. A novel measure of edge centrality in social networks. Knowledge-Based Systems, 30, 136-150.
DOI: 10.1016/j.knosys.2012.01.007
