<p>Technically yes, the graph you describe is one 2-clique percolated community. However, this is a reduced case, since a 2-clique is no more than an edge, and so a 2-clique percolated community is just a connected component.</p>

<p>For k > 2, clique percolation results in communities that are only detectable using this method. The example in Wiki uses 4-cliques.</p>

CC BY-SA 3.0
2014-12-10T08:31:18.760Z
2014-12-10T08:47:54.590Z
2014-12-10T08:47:54.590Z
Qwerty
<p>So I can find the <a href="http://en.wikipedia.org/wiki/Clique_percolation_method" rel="nofollow">Wiki</a> article okay, as I think I understand that this is a definition of a special community in a graph.  However their image in Fig. 1 confuses me from the description.</p>

<p>As I understand it, the definition of a clique percolation within a graph is:</p>

<ol>
<li>You have a set of k-maximal cliques, which contain k nodes.</li>
<li>You are said to have k-adjacent cliques if each k-maximal cliques are connected by (k-1)-nodes.</li>
</ol>

<p>So a graph that was (1)&lt;-->(2)&lt;-->(3) could be considered a community because it has 2 2-maximal cliques, [[1,2], [2,3]], and each of them are connected by 1 vertex. </p>

<p>Am I reading the Wiki correctly, because I feel like I'm missing something. Thanks for any help your able to lend.</p>

<graph-theory><graph-algorithms><clique>
Help with the definition of clique percolation
Nicholas
# Help with the definition of clique percolation

(Asked by: username_0 on 2013-04-13)

So I can find the [Wiki](http://en.wikipedia.org/wiki/Clique_percolation_method) article okay, as I think I understand that this is a definition of a special community in a graph. However their image in Fig. 1 confuses me from the description.

As I understand it, the definition of a clique percolation within a graph is:

1. You have a set of k-maximal cliques, which contain k nodes.
2. You are said to have k-adjacent cliques if each k-maximal cliques are connected by (k-1)-nodes.

So a graph that was (1)<-->(2)<-->(3) could be considered a community because it has 2 2-maximal cliques, [[1,2], [2,3]], and each of them are connected by 1 vertex.

Am I reading the Wiki correctly, because I feel like I'm missing something. Thanks for any help your able to lend.

**Tags:** graph-theory, graph-algorithms, clique


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## 1 answers

### Answer by username_1 on 2014-12-10. Score: 1

Technically yes, the graph you describe is one 2-clique percolated community. However, this is a reduced case, since a 2-clique is no more than an edge, and so a 2-clique percolated community is just a connected component.

For k > 2, clique percolation results in communities that are only detectable using this method. The example in Wiki uses 4-cliques.


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