# κ-Path Centrality

#### Definition

**κ-path edge centrality**

For each edge e of a graph G = (V,E), the κ-path edge centrality L

^{κ}(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, σ

^{κ}

_{s}(e) is the number of κ-paths originating from s and traversing the edge e and, finally, σ

^{κ}

_{s}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**

#### 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