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Find Network Components

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Find Network Components

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31 May 2013 (Updated )

Find network components, sizes, and lists of member nodes.

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Description

Given an undirected network represented by an adjacency matrix, we may wish to find that network's
- largest component
- number of components
- list of which nodes are in which component together.
This code computes these rapidly (linear in the number of nodes) and accurately. The code is commented so that if you wish to modify it, you may do so.

INPUT:
1. Network adjacency matrix.

OUTPUTS:
1. Number of network components
2. Sizes of network components (sorted, descending)
3. Membership list of each component (sorted by component size, descending).

Code includes a couple examples of usage at the top. I have tested this in R2014a, but it uses nothing fancy, and I believe it to be backward compatible for many years.

Required Products MATLAB
MATLAB release MATLAB 8.1 (R2013a)
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Comments and Ratings (6)
26 Apr 2014 Alphab

Great work!

26 Apr 2014 Wolfgang Schwanghart

Hi, you might also want to take a look at Tim Davis' function find_components: http://www.mathworks.com/matlabcentral/fileexchange/21366-find-components
find_components uses the builtin function dmperm to find connected components.

24 Apr 2014 Daniel Larremore

Iro, suggestion appreciated. The code removes diagonal elements already, but I have edited the example anyway.

24 Mar 2014 Iro

Hi, it seems to work for a given adjacency matrix, but you might want to edit the example of creating a random one because it is possible that it generates ones in the diagonal.

13 Aug 2013 Li  
30 Jul 2013 TCH  
Updates
05 Jun 2013

Fixed typo in description.

24 Apr 2014

Fixed typos (clarity), removed possibility of self-edges in the example (clarity), changed instances of "cluster" to "component" in comments and variable names (clarity and correctness), and sorted outputs by component sizes (ease of use).

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