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Genes communicate with each other through different regulatory effects, whichlead to the emergence of complex structures in cells, and such structures areexpected to be different for normal and cancerous cells. To study breast cancerdifferences, we have investigated the Gene Regulatory Network (GRN) of cells asinferred from RNA-sequencing data. The GRN is a signed weighted networkcorresponding to the inductive or inhibitory interactions. Here we focus on aparticular of motifs in the GRN, the triangles, which are imbalanced if thenumber of negative interactions are odd. By studying the stability ofimbalanced triangles in the GRN, we show that the network of cancerous cellshas fewer imbalanced triangles compared to normal. Moreover, in the normalcells, imbalanced triangles are isolated from the main part of the network,while such motifs are part of the network's giant component in cancerous cells.Our result demonstrates that due to genes' collective behavior the complexstructures are different in cancerous cells from those in normal ones.

Stability of Imbalanced Triangles in Gene Regulatory Networks of Cancerous and Normal Cells