# Measures of Node Prominence on a Network

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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.

Contributed by: Seth J. Chandler (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## 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 powerâ€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.

## Permanent Citation

"Measures of Node Prominence on a Network"

http://demonstrations.wolfram.com/MeasuresOfNodeProminenceOnANetwork/

Wolfram Demonstrations Project

Published: March 7 2011