Centrality

Centrality measures¶

Degree¶

The simplest measure. A node’s degree is just the count of direct connections (edges) it has. A node connected to 10 others has degree 10. It tells you who has the most immediate neighbors, but nothing about the quality or reach of those connections.

Eigenvector¶

Captures the idea that not all connections are equal — being connected to well-connected nodes makes you more important. A node’s eigenvector centrality score is proportional to the sum of its neighbors’ scores, solved simultaneously across the whole network (hence the eigenvector). Google’s original PageRank algorithm is a well-known variant of this idea. It rewards nodes that are connected to other influential nodes, not just many nodes.

Betweenness¶

Measures how often a node sits on the shortest path between other pairs of nodes. You find the shortest route between every pair of nodes in the network, then count how many of those routes pass through each node. A node with high betweenness is a critical bridge or bottleneck — information or flow passing across the network likely goes through it. Removing a high-betweenness node can fragment the network.

Strength¶

An extension of degree for weighted networks. Instead of counting edges, you sum the weights of all edges attached to a node. For example, if connections represent how often two people email each other, strength captures total communication volume — not just how many contacts you have, but how active those relationships are.

Comparison¶