clique

I am trying to find maximal cliques for a set of items. Currently I am using networkx library of python and using find_cliques() function to find all the maximal cliques as below: import newtworkx as nx G = nx.Graph() E = [[1,2], [1,3], [1,4], [2,3], [2,4], [3,4], [2,6], [2,5], [5,6]] G.add_edges_from(E) #G.edges() lst = list(nx.find_cliques(G)) lst Out [] : [[2, 1, 3, 4], [2, 5, 6]] But what I am actually expecting is to find maximal cliques and then remove the nodes which were in the maximal clique graph, and then again find maximal clique out of the nodes left after previous removal. For

I have this problem and I need help with it, this is my code: cliques=[clique for clique in nx.find_cliques(GC) if len(clique)>2] for clique in cliques: if len (clique)==3: GC.remove_edge() print "Clique to appear: ",clique #draw the graph nx.draw(GC) plt.show() first I searched in my graph to find cliques, after that I test if the clique of length 3, if its true I want to delete one edge So I can eliminate complete-graph(3). How can I do that? Thanks I think the trickiest problem here is dealing with shared edges. You don't want to search for cliques each time you remove an edge, and yet you

Given a 2D array of Boolean values I want to find all patterns that consist of at least 2 columns and at least 2 rows. The problem is somewhat close to finding cliques in a graph . In the example below green cells represent "true" bits, greys are "false". Pattern 1 contains cols 1,3,4 and 5 and rows 1 and 2. Pattern 2 contains only columns 2 and 4, and rows 2,3,4. Business idea behind this is finding similarity patterns among various groups of social network users. In real world number of rows can go up to 3E7, and the number of columns up to 300. Can't really figure out a solution other than

for a college project I'm trying to implement the Bron–Kerbosch algorithm , that is, listing all maximal cliques in a given graph. I'm trying to implement the first algorithm (without pivoting) , but my code doesn't yield all the answers after testing it on the Wikipedia's example , my code so far is : # dealing with a graph as list of lists graph = [[0,1,0,0,1,0],[1,0,1,0,1,0],[0,1,0,1,0,0],[0,0,1,0,1,1],[1,1,0,1,0,0],[0,0,0,1,0,0]] #function determines the neighbors of a given vertex def N(vertex): c = 0 l = [] for i in graph[vertex]: if i is 1 : l.append(c) c+=1 return l #the Bron-Kerbosch

By executing Networkx triadic_census Algorithm, I'm able to get the dictionary of the number of nodes falling on each type of triadic census triad_census_social=nx.triadic_census(social_graph.to_directed()) Now, I'd like to return the list of triads, who all follow the pattern of census code "201", "120U", or any one of the 16 existing types. How can I get those node lists under a census count? There is no function in networkx that allow you to do it, so you should implement it manually. I modified the networkx.algorithms.triads code for you to return triads, not their count: import networkx

Subgraph isomorphism We have the graphs G_1=(V_1,E_1), G_2=(V_2,E_2). Question : Is the graph G_1 isomorphic to a subgraph of G_2 ? (i.e. is there a subset of vertices of G_2, V ⊆ V_2 and subset of the edges of G_2, E ⊆ E_2 such that |V|=|V_1| and |E|=|E_1| and is there a one-to-one matching of the vertices of G_1 at the subset of vertices V of G_2, f:V_1 -> V such that {u,v} ∈ E_1 <=> { f(u),f(v) } ∈ E) Show that the problem Subgraph isomorphism belongs to NP. Show that the problem is NP-complete reducing the problem Clique to it. (Hint: consider that the graph G_1 is complete) I have tried