Graph-isomorphism connections for NetOTC

Establish general connections between the NetOTC method for comparing directed graphs via optimal transition couplings of random walks and the graph isomorphism problem.

Background

NetOTC is described as a method for comparing and aligning directed graphs by computing an optimal transition coupling of their random walks using a vertex-based cost function. Unlike the optimal graph joining framework studied in the paper, NetOTC imposes no symmetry constraints on graph weights or transition couplings, and its optimization problem is not generally a linear program.

The paper states that broad theoretical connections between NetOTC and graph isomorphism have not yet been established. Developing such connections would clarify the isomorphism-detection and identification capabilities of NetOTC.

References

Absent symmetry constraints, the NetOTC problem is not a linear program, and general connections between NetOTC and graph isomorphism are not known at the present time.

— Optimal graph joining with applications to isomorphism detection and identification  (2511.14862 - Hoàng et al., 18 Nov 2025) in Section 5.1, “Relation with Weisfeiler-Lehman and NetOTC”