# BridgeRank

#### Definition

This method improved closeness centrality by utilizing the local structure of nodes and presents a new ranking algorithm, called $BridgeRank$ centrality. The proposed method computes local centrality value for each node. For this purpose, at first, communities are detected and the relationship between communities is completely ignored. Then, by applying a centrality in each community, only one best critical node from each community is extracted. Finally, the nodes are ranked based on computing the sum of the shortest path length of nodes to obtained critical nodes.

$$BridgeRank(v)= \left[ {\underset{u\in \Gamma_k}{\sum}} d(v,u)\right ]^{-1} , v=1...n$$

where, $Г_k$ is the set of $k$ cores and $d(v,u)$ is the shortest path between node $v$ and $u$.

This method utilized the local and global structure and bridging role of nodes and performs better than other well-known centrality measures.

$$BridgeRank(v)= \left[ {\underset{u\in \Gamma_k}{\sum}} d(v,u)\right ]^{-1} , v=1...n$$

where, $Г_k$ is the set of $k$ cores and $d(v,u)$ is the shortest path between node $v$ and $u$.

This method utilized the local and global structure and bridging role of nodes and performs better than other well-known centrality measures.

#### References

- Salavati C., Abdollahpouri A., Manbari Z., 2018. BridgeRank: A novel fast centrality measure based on local structure of the network. Physica A: Statistical Mechanics and its Applications, 496, pp.635-653. DOI: 10.1016/j.physa.2017.12.087