How is centrality measured in web graph analysis?

Centrality in web graph analysis is typically measured using degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality.

In web graph analysis, centrality measures are used to identify the most important nodes within a graph. These measures provide a way of detecting the nodes that have the most influence over the network, based on their connections. There are four main types of centrality measures: degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality.

Degree centrality is the simplest measure. It counts the number of edges that a node has, which in the context of a web graph, means the number of links a webpage has. A webpage with a high degree centrality is one that has many links to other pages. This is often interpreted as a measure of immediate influence or popularity.

Closeness centrality measures how close a node is to all other nodes in the network. In a web graph, this would mean how few clicks it would take to reach any other webpage from a given webpage. A webpage with high closeness centrality can access and spread information quickly through the network.

Betweenness centrality measures the extent to which a node lies on paths between other nodes. In terms of a web graph, a webpage with high betweenness centrality would be one that is often on the shortest path between two other webpages. This could be interpreted as a measure of control or brokerage over information flow in the network.

Eigenvector centrality is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes. In the context of a web graph, a webpage with high eigenvector centrality is not just linked to many other pages, but is linked to pages that are themselves important.

In conclusion, centrality measures in web graph analysis provide a way of identifying the most influential nodes within a network, based on their connections. These measures can be used to understand the structure and dynamics of the network, and to identify key players or influencers within it.