Graph Utilities Package
GRAPH UTILITIES PACKAGE SYMBOL

ClosenessCentrality

ClosenessCentrality[g]
finds the closeness centrality.

DetailsDetails

  • To use , you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • The closeness centrality of a vertex u is defined as the inverse of the sum of the distance from u to all other vertices. The closeness centrality of a vertex in a disconnected graph is based on the closeness centrality of the component where this vertex belongs.
  • The following options can be given:
  • WeightedTruewhether edge weight is to be used in calculating distance
    NormalizeFalsewhether to normalize the output

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

In[1]:=
Click for copyable input

This defines a small graph:

In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=

This shows that vertex 2, being at the center of this graph, has a higher closeness centrality:

In[4]:=
Click for copyable input
Out[4]=
In[1]:=
Click for copyable input

This defines a disconnected graph and finds the closeness centrality:

In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
Out[4]=

Scope (1)Scope (1)

Options (1)Options (1)

Applications (1)Applications (1)

Top
Send Feedback
Mathematica 9 is now available!

400+ new features, including the new Wolfram Predictive Interface, social network analysis, enterprise CDF deployment, and more »

Try Now
Buy/Upgrade
New to Mathematica? Find your learning path »
Have a question? Ask support »