Novel Model for Cascading Failure Based on Degree Strength and Its Application in Directed Gene Logic Networks

A novel model for cascading failures in a directed logic network based on the degree strength at a node was proposed. The definitions of in-degree and out-degree strength of a node were initially reconsidered, and the load at a nonisolated node was proposed as the ratio of in-degree strength to out-degree strength of the node. The cascading failure model based on degree strength was applied to the logic network for three types of cancer including adenocarcinoma of lung, prostate cancer, and colon cancer based on their gene expression profiles. In order to highlight the differences between the three networks by the cascading failure mechanism, we used the largest-scale cascades and the cumulative cascade probability to depict the damage. It was found that the cascading failures caused by hubs are usually larger. Furthermore, the result shows that propagations against the networks were correlated with the structures motifs of connected logical doublets. Finally, some genes were selected based on cascading failure mechanism. We believe that these genes may be involved in the occurrence and development of three types of cancer.