Network Centrality Using Eigenvectors

​
number of nodes
4
show edge weights
show node centrality
adjacency matrix A:
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
centrality matrix x:
1.61803
1.61803
1.
1.
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
·
1.61803
1.61803
1.
1.
=
2.61803
2.61803
1.61803
1.61803
= 1.61803
1.61803
1.61803
1.
1.
​
Ax = λx
Eigenvector centrality is one method of computing the "centrality", or approximate importance, of each node in a graph. The assumption is that each node's centrality is the sum of the centrality values of the nodes that it is connected to. The nodes are drawn with a radius proportional to their centrality. The adjacency matrix and centrality matrix for the solution are shown. The centrality matrix is an eigenvector of the adjacency matrix such that all of its elements are positive.

External Links

Adjacency Matrix (Wolfram MathWorld)
Eigenvector (Wolfram MathWorld)
Network (Wolfram MathWorld)

Permanent Citation

Brian Levinstein
​
​"Network Centrality Using Eigenvectors"​
​http://demonstrations.wolfram.com/NetworkCentralityUsingEigenvectors/​
​Wolfram Demonstrations Project​
​Published: December 7, 2009