# Local Bridging Centrality

#### Definition

The local bridging centrality was a variant of global bridging centrality which can be calculated locally requiring only limited local neighborhood graph information

$$LBC=C_{lbet}*\beta_c$$

were $C_{lbet}$ is computationally simplified over the calculation of global betweenness centrality and only requires the I-hop adjacency matrix, while the coefficient $\beta_c$ takes into account local bridging structural features of the node and defined as fallows:

$$\beta_c={{1\over d(v)} \over \sum_{i\in N(v)}{1\over d(i)}}$$

were $d(v)$ is the degree of node $v$, and $N(v)$ is the set of graph neighbors of node $v$. The bridging coefficient attempts to model how well situated a node is between other high degree nodes within a localized topology.

Localized centrality calculations can reduce both communication and computation complexity and there are a myriad of potential applications. It is expected that the concept of localized bridging centrality can improve existing distributed relay or optimization algorithms

$$LBC=C_{lbet}*\beta_c$$

were $C_{lbet}$ is computationally simplified over the calculation of global betweenness centrality and only requires the I-hop adjacency matrix, while the coefficient $\beta_c$ takes into account local bridging structural features of the node and defined as fallows:

$$\beta_c={{1\over d(v)} \over \sum_{i\in N(v)}{1\over d(i)}}$$

were $d(v)$ is the degree of node $v$, and $N(v)$ is the set of graph neighbors of node $v$. The bridging coefficient attempts to model how well situated a node is between other high degree nodes within a localized topology.

Localized centrality calculations can reduce both communication and computation complexity and there are a myriad of potential applications. It is expected that the concept of localized bridging centrality can improve existing distributed relay or optimization algorithms