In this lecture, we will

• Introduce the notion of centrality .
• Introduce degree centrality and eigenvector centrality and study approaches to computing these measures.
• Understand how eigenvector centrality does not work for directed acyclic graphs (DAGs) and introduce Katz centrality as a better notion of centrality than eigenvector centrality.
• Further introduce page-rank centrality to fix issues with Katz centrality.
• Combine inward and outward importances in one iterative algorithm to compute hubs and authorities scores of nodes in a graph.
• Introduce closeness and betweenness centrality and learn how to compute them.

I. Centrality Measures – Introduction

1. Find important nodes

Centrality measure: a measure that captures importance of a nodes’s position in the network

There are many different centrality measures:

• degree centrality (indegree/ outdegree)
• “propagated” degree centrality (score that is proportional to the sum of the score of all neighbors)
• closeness centrality
• betweeness centrality

Choice of centrality measure depends on application!

In a friendship network:

• high degree centrality: most popular person