# Semi Local Centrality

#### Definition

The local centrality C

The local centrality is proposed aiming at identifying the influencers in undirected network, it can be applied to directed network as well with a modified definition of N(w). Of course, for directed network, N(w) should be the number of the nearest and next nearest upstream nodes of node w.

Local centrality measure is likely to be more effective to identify influential nodes than degree centrality measure as it utilizes more information, while it has much lower computational complexity than the betweenness and closeness centralities.

_{L}(v) of node v is defined as: where Γ(u) is the set of the nearest neighbors of node u and N(w) is the number of the nearest and the next nearest neighbors of node w.The local centrality is proposed aiming at identifying the influencers in undirected network, it can be applied to directed network as well with a modified definition of N(w). Of course, for directed network, N(w) should be the number of the nearest and next nearest upstream nodes of node w.

Local centrality measure is likely to be more effective to identify influential nodes than degree centrality measure as it utilizes more information, while it has much lower computational complexity than the betweenness and closeness centralities.

#### Computational complexity

O(n(k)

^{2})#### Software

#### References

- CHEN, D., LÜ, L., SHANG, M.-S., ZHANG, Y.-C. & ZHOU, T. 2012. Identifying influential nodes in complex networks. Physica A: Statistical Mechanics and its Applications, 391, 1777-1787. DOI: 10.1016/j.physa.2011.09.017