Background:Comparing directed networks using the alignment-free technique offers the advantage of detecting topologically similar regions that are independent of the network size or node identity.

Objective:We propose a novel method to compare directed networks by decomposing the network into small modules, the so-called network subgraph approach, which is distinct from the network motif approach because it does not depend on null model assumptions.

Methods:We developed an alignment-free algorithm called the Subgraph Identification Algorithm (SIA), which could generate all subgraphs that have five connected nodes (5-node subgraph). There were 9,364 such modules. Then, we applied the SIA method to examine 17 cancer networks and measured the similarity between the two networks by gauging the similarity level using Jensen- Shannon entropy (HJS).

Results:We identified and examined the biological meaning of 5-node regulatory modules and pairs of cancer networks with the smallest HJS values. The two pairs of networks that show similar patterns are (i) endometrial cancer and hepatocellular carcinoma and (ii) breast cancer and pathways in cancer. Some studies have provided experimental data supporting the 5-node regulatory modules.

Conclusion:Our method is an alignment-free approach that measures the topological similarity of 5-node regulatory modules and aligns two directed networks based on their topology. These modules capture complex interactions among multiple genes that cannot be detected using existing methods that only consider single-gene relations. We analyzed the biological relevance of the regulatory modules and used the subgraph method to identify the modules that shared the same topology across 2 cancer networks out of 17 cancer networks. We validated our findings using evidence from the literature.