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

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... tween 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.