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