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Two graph theoretic concepts—clique and bipartite graphs—are explored to identify the network biomarkers for cancer at the gene network level. The rationale is that a group of genes work together by forming a cluster or a clique-like structures to initiate a cancer. After initiation, the disease signal goes to the next group of genes related to the second stage of a cancer, which can be represented as a bipartite graph. In other words, bipartite graphs represent the cross-talk among the genes between two disease stages. To prove this hypothesis, gene expression values for three cancers— breast invasive carcinoma (BRCA), colorectal adenocarcinoma (COAD) and glioblastoma multiforme (GBM)—are used for analysis. First, a co-expression gene network is generated with highly correlated gene pairs with a Pearson correlation coefficient ≥ 0.9. Second, clique structures of all sizes are isolated from the co-expression network. Then combining these cliques, three different biomarker modules are developed—maximal clique-like modules, 2-clique-1-bipartite modules, and 3-clique-2-bipartite modules. The list of biomarker genes discovered from these network modules are validated as the essential genes for causing a cancer in terms of network properties and survival analysis. This list of biomarker genes will help biologists to design wet lab experiments for further elucidating the complex mechanism of cancer.

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