# Barycenter Centrality

#### Definition

Barycenter Centrality for vertex v defined as:

There are 2 types of distance centrality scores – Closeness Centrality and Barycenter Centrality.

Closeness scores are calculated using the formula 1 / (average distance from vertex v to all other vertices) and Barycenter scores are calculated as 1 / (total distance from vertex v to all other vertices).

More central nodes in a connected component will have smaller overall shortest paths, and 'peripheral' nodes on the network will have larger overall shortest paths.

Runing this ranker on a graph with more than one connected component will arbitarily mix nodes from both components. For this reason you should probably run this ranker on one component only.

- 1 / (total distance from v to all other vertices)

There are 2 types of distance centrality scores – Closeness Centrality and Barycenter Centrality.

Closeness scores are calculated using the formula 1 / (average distance from vertex v to all other vertices) and Barycenter scores are calculated as 1 / (total distance from vertex v to all other vertices).

More central nodes in a connected component will have smaller overall shortest paths, and 'peripheral' nodes on the network will have larger overall shortest paths.

Runing this ranker on a graph with more than one connected component will arbitarily mix nodes from both components. For this reason you should probably run this ranker on one component only.

#### Requirements

Require connected and strongly connected network.

#### Software

#### References

- Viswanath, M., 2009. Ontology-based automatic text summarization (Doctoral dissertation, uga).

https://athenaeum.libs.uga.edu/handle/10724/26178