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Closeness centrality

Closeness Centrality

In the field of social network analysis, centrality measures are used to determine the importance or influence of individual nodes within a network. One of the key measures is closeness centrality, which evaluates how close a node is to all other nodes in the network. This report introduces the concepts of paths and geodesic lines and explains the meaning and interpretation of closeness centrality.

Key definitions

  • Path: A path in a network is a sequence of edges that connect a sequence of nodes. For example, if A is connected to C and C is connected to B, then A → C → B is a path.

  • Geodesic Line: This is the shortest possible path between two nodes. While multiple paths may connect two nodes, the geodesic is the one with the fewest edges. For example, if A is directly connected to B, that single connection (A → B) is the geodesic path, even if there exists a longer alternative like A → C → B.

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Closeness centrality quantifies how near a node is to all other nodes in the network. It is calculated as the reciprocal of the sum of the shortest path lengths from that node to every other node.

Nodes with high closeness centrality can reach other nodes more quickly, making them effective for spreading information or influencing others. In contrast, nodes with low closeness centrality are more isolated and slower to interact with the entire network.

For example, a central manager in an organization with high closeness centrality may communicate efficiently with all departments. A remote or specialized employee, on the other hand, might have low closeness centrality due to limited connections.

Visual example

In a sample network diagram:

  • Node A has short paths to most other nodes, indicating high closeness centrality.

  • Node F, located at the edge, must traverse longer paths to reach others, resulting in low closeness centrality.

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Conclusion

Closeness centrality is a valuable metric in social network analysis for identifying individuals who are well-positioned to access and disseminate information quickly. It supports decision-making in organizational communication, marketing, epidemiology, and many other domains where network structure influences behavior and outcomes.

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