# Leverage Centrality

#### Definition

Leverage centrality considers the degree of a node relative to its neighbors and operates under the principle that a node in a network is central if its immediate neighbors rely on that node for information.

Leverage centrality is a measure of the relationship between the degree of a given node (k

Leverage centrality is a measure of the relationship between the degree of a given node (k

_{i}) and the degree of each of its neighbors (k_{j}), averaged over all neighbors (N_{i}), and is defined as shown below. A node with negative leverage centrality is influenced by its neighbors, as the neighbors connect and interact with far more nodes. A node with positive leverage centrality, on the other hand, influences its neighbors since the neighbors tend to have far fewer connections.#### Software

#### References

- JOYCE, K. E., LAURIENTI, P. J., BURDETTE, J. H. & HAYASAKA, S. 2010. A new measure of centrality for brain networks. PLoS One, 5, e12200.