Create new graph of all nodes that are a part of 4-node clique

[Curtis Hampton]

I have a network that I would like to bound by clique, but I haven't quite figured out how to do this correctly. I am able to do this same process using k-cores, but not sure what the right process for creating a graph with only cliques in it.

I was hoping if I show my process for find subgraphs using the k_core function, someone could help me alter my process to find subgraphs using the clique function.

To start, I create a graph, I'll use the karate club one:

In [1]: import networkx as nx

In [2]: g = nx.karate_club_graph()

Plot to graph in iPython:

In [3]: pylab inline
Populating the interactive namespace from numpy and matplotlib

In [4]: nx.draw(g)

Next, I find all edges that are within the 4-core (have 4 or more edges):

In [5]: g_4k_edges = nx.k_core(g, k=4).edges()

Add those edges to a new graph:

In [6]: g_4k = nx.Graph() In [7]: g_4k.add_edges_from(g_4k_edges)

Plot the 4-core graph:

In [8]: nx.draw(g_4k)

Any idea on how to do this, but instead of using k-cores to bound the network, use cliques that have 4 or more vertices?

[Aric Hagberg]

Maybe networkx.find_cliques() will help you?
Aric

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[Curtis Hampton]

Thanks Aric.

I've tried to figure out how I could use find_cliques() and find_cliques_recursive() to answer this question, but haven't been able to work it out yet.


import networkx as nx

# load graph as g
g = nx.karate_club_graph()

# find cliques in g
cliques = nx.find_cliques(g)

I'm not sure what to do next to limit my graph to only cliques of 4 or more.  I tried adding .edges() to the end of my last command to return all the edges found, and then adding those edges to a blank graph, but I received an error.

[Daπid]

On 12 August 2014 01:59, Curtis Hampton <curtisl...@gmail.com> wrote:

I'm not sure what to do next to limit my graph to only cliques of 4 or more.  I tried adding .edges() to the end of my last command to return all the edges found, and then adding those edges to a blank graph, but I received an error.

 

All the clicques of k nodes or more are inside the (k-1)-core of the network; and vice versa. So, take the core and find cliques there.

/David.