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Measures of Node Prominence on a Network

Various measures exist to describe the prominence of nodes on a network or, equivalently, vertices on a graph. This Demonstration shows several of those measures for a set of sample networks by relating the size of each node to its prominence. The user can explore how the embedding of a network relates to the location of its prominent nodes.

SNAPSHOTS

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DETAILS

The first network is the tree structure of Mathematica's solution to a quadratic equation. The second network is the proximity structure of regions in the board game of "Risk." The third network is a sample of an airline network. The fourth and fifth networks are randomly created with power-law distributions of outgoing vertices.
Snapshot 1: measuring the page rank of the "Risk" network using a spring embedding.
Snapshot 2: measuring the closeness centrality of a partial airline network using a layered digraph drawing.
Snapshot 3: measuring the total degrees of a random network using a linear embedding.
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