Centrality Measures in Networks

Centrality measures help us understand the importance of nodes in networks, revealing how they connect and influence each other. These concepts are crucial for navigating social networks, information flow, and the dynamics of our networked lives.

1. Degree Centrality

   • Measures the number of direct connections a node has in a network.
   • High degree centrality indicates a node is a popular or influential point in the network.
   • Useful for identifying key players or hubs in social networks, such as influencers.
   • Does not account for the quality or influence of a node's connections.

2. Closeness Centrality

   • Assesses how quickly a node can access other nodes in the network.
   • Calculated based on the average shortest path length from a node to all other nodes.
   • Nodes with high closeness centrality can spread information quickly and efficiently.
   • Important for understanding the potential for influence and information dissemination.

3. Betweenness Centrality

   • Measures the extent to which a node lies on the shortest paths between other nodes.
   • High betweenness centrality indicates a node acts as a bridge or intermediary in the network.
   • Critical for identifying nodes that control information flow and connectivity.
   • Can highlight potential vulnerabilities in a network if key nodes are removed.

4. Eigenvector Centrality

   • Evaluates a node's influence based on the quality and influence of its connections.
   • A node is considered important if it is connected to other important nodes.
   • Provides a more nuanced view of centrality compared to degree centrality.
   • Useful in social networks to identify influential individuals beyond mere connections.

5. PageRank

   • Developed by Google to rank web pages based on their importance and link structure.
   • Similar to eigenvector centrality, it considers both the quantity and quality of links.
   • Nodes receive higher scores if they are linked to by other high-scoring nodes.
   • Widely used in search engines and social media to determine relevance and authority.

6. Katz Centrality

   • Extends degree centrality by considering the total number of paths to a node, weighted by their length.
   • Accounts for both direct and indirect connections, allowing for a broader view of influence.
   • Nodes with high Katz centrality can reach others through multiple pathways.
   • Useful in networks where indirect connections are significant for influence.

7. Hub and Authority Scores

   • Part of the HITS (Hyperlink-Induced Topic Search) algorithm, distinguishing between hubs and authorities.
   • Hubs are nodes that link to many other nodes, while authorities are nodes that are linked to by many hubs.
   • Helps identify nodes that serve as valuable resources (authorities) and those that act as connectors (hubs).
   • Important for understanding the structure of networks, especially in web and information systems.