Centrality in Network Analysis

Overview

• Centrality measures the influence or significance of a node within a network.
• Significance varies based on the network type.
• Centrality indices help identify what makes a node important.

Importance of Centrality

• Degree of connectivity is the simplest measure of centrality.
  • Measures how many nodes a node is connected to versus potential connections.
  • Focuses on local network environment.
• Centrality provides a more complex understanding of a node's position in a network.
• Significance can be seen as the flow of resources through a node and its replaceability.

Key Metrics for Centrality

1. Degree Centrality
   • Primary metric to define a node's significance locally.
2. Closeness Centrality
   • Measures how quickly a node can reach other nodes.
   • Defined as the reciprocal of farness (sum of distances to all other nodes).
   • Indicates how fast information can spread from the node.
3. Betweenness Centrality
   • Captures a node's role as a bridge between groups of nodes.
   • Quantifies how often a node acts as a bridge on shortest paths.
4. Prestige/Eigenvector Centrality
   • Focuses on the significance of connected nodes.
   • Connections to highly connected nodes are valued more.
   • Used by web search engines to rank website importance.

Application

• Different metrics provide various perspectives on node centrality.
• Visual representation using color coding (dark blue to red) to depict node ranking helps in understanding the different insights each metric provides.

Summary

• Understanding centrality helps evaluate a node's influence and role in the network.
• Each metric provides unique insights into network dynamics and node significance.
• Node centrality is relative and context-dependent.