arrays,algorithm,pattern-matching,np,clique

This is (equivalent to) asking for all bicliques (complete bipartite subgraphs) larger than a certain size in a bipartite graph. Here the rows are the vertices of one part A of the graph, and the columns are the vertices of the other part B, and there is an edge between...

python,algorithm,tree,graph-theory,clique

To construct a non-nice (in general) tree decomposition of a chordal graph: find a perfect elimination ordering, enumerate the maximal cliques (the candidates are a vertex and the neighbors that appear after it in the ordering), use each clique as a decomposition node and connect it to the next...

python,postgresql,plpython,clique,connected-components

With networkX: import networkx as nx G1=nx.Graph() G1.add_edges_from([("a","b"),("b","c"),("c","d"),("d","e"),("f","g")]) sorted(nx.connected_components(G1), key = len, reverse=True) giving: [['a', 'd', 'e', 'b', 'c'], ['f', 'g']] You have to check the fastest algorithm now ... OP: This works great! I have this in my PostgreSQL database now. Just organize pairs into a two-column table, then...

algorithm,np-complete,clique,vertex-cover

If there's two vertices from the clique not in a set, then the edge between them isn't covered, so any cover must have at least n-1 vertices. Any subset of n-1 vertices is a cover, trivially.

java,cluster-analysis,elki,clique

Note that CLIQUE produces overlapping clusters. Elements can be in 0 to many clusters at the same time. If you choose your parameters badly (and CLIQUE parameters seem to be really hard to choose), you will get weird results. In your case, it seems to be 11 clusters, despite your...