PMC:1481596 / 32749-33903 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1481596","sourcedb":"PMC","sourceid":"1481596","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1481596","text":"A compact boolean representation of functional groups\nRecall that a functional group corresponds to a maximal clique in the modified protein interaction network, with modifications being addition of edges between every pair of weak siblings and then addition of edges that eliminate all the squares in the graph. The edge addition is such that no maximal clique in the modified graph contains an induced P4 formed entirely by the added edges. Following lemma guarantees that every functional group is a cograph and therefore admits a compact Boolean representation.\nLemma For every functional group, a subgraph of the original graph induced by the members of the group contains an induced P4 if and only if the set of edges added by our algorithm contains an induced P4.\nProof The argument follows from Figure 5. Indeed, (v1, v2, v3, v4) is a P4 in the original graph if and only if (v3, v1, v4, v2) is a P4 formed by the added edges.\nFigure 5 P4. A P4 in the subgraph induced by the members of a functional group corresponds to a P4 in the set of added edges. Solid lines correspond to the original edges and dashed lines correspond to the added edges.","divisions":[{"label":"title","span":{"begin":0,"end":53}},{"label":"p","span":{"begin":54,"end":565}},{"label":"p","span":{"begin":566,"end":770}},{"label":"p","span":{"begin":771,"end":934}},{"label":"label","span":{"begin":935,"end":943}}],"tracks":[]}