Hepatocellular carcinoma (HCC) is one of the most common lethal cancers worldwide and is often related to late diagnosis and poor survival outcome. More evidence is demonstrating that gene-based prognostic models can be used to predict high-risk HCC patients. Therefore, our study aimed to construct a novel prognostic model for predicting the prognosis of HCC patients. We used multivariate Cox regression model with three hybrid penalties approach including least absolute shrinkage and selection operator (Lasso), adaptive lasso and elastic net algorithms for informative prognostic-related genes selection. Then, the best subset regression was used to identify the best prognostic gene signature. The prognostic gene-based risk score was constructed using the Cox coefficient of the prognostic gene signature. The model was evaluated by Kaplan–Meier (KM) and receiver operating characteristic curve (ROC) analyses. A novel four-gene signature associated with prognosis was identified and the risk score was constructed based on the four-gene signature. The risk score efficiently distinguished the patients into a high-risk group with poor prognosis. The time-dependent ROC analysis revealed that the risk model had a good performance with an area under the curve (AUC) of 0.780, 0.732, 0.733 in 1-, 2- and 3-year prognosis prediction in The Cancer Genome Atlas (TCGA) dataset. Moreover, the risk score revealed a high diagnostic performance to classify HCC from normal samples. The prognosis and diagnosis prediction performances of risk scores were verified in external validation datasets. Functional enrichment analysis of the four-gene signature and its co-expressed genes involved in the metabolic and cell cycle pathways was constructed. Overall, we developed a novel-gene-based prognostic model to predict high-risk HCC patients and we hope that our findings can provide promising insight to explore the role of the four-gene signature in HCC patients and aid risk classification.

Biological processes are based on molecular networks, which exhibit biological functions through interactions of genetic elements or proteins. This study presents a graph-based method to characterize molecular networks by decomposing the networks into directed multigraphs: network subgraphs. Spectral graph theory, reciprocity and complexity measures were used to quantify the network subgraphs. Graph energy, reciprocity and cyclomatic complexity can optimally specify network subgraphs with some degree of degeneracy. Seventy-one molecular networks were analyzed from three network types: cancer networks, signal transduction networks, and cellular processes. Molecular networks are built from a finite number of subgraph patterns and subgraphs with large graph energies are not present, which implies a graph energy cutoff. In addition, certain subgraph patterns are absent from the three network types. Thus, the Shannon entropy of the subgraph frequency distribution is not maximal. Furthermore, frequently-observed subgraphs are irreducible graphs. These novel findings warrant further investigation and may lead to important applications. Finally, we observed that cancer-related cellular processes are enriched with subgraph-associated driver genes. Our study provides a systematic approach for dissecting biological networks and supports the conclusion that there are organizational principles underlying molecular networks.