Symmetry-driven network reconstruction through pseudobalanced coloring optimization

Symmetries found through automorphisms or graph fibrations provide important insights in network analysis. identify clusters of robust synchronization the which improves understanding functionality complex biological systems. Network symmetries can be determined by finding a {\it balanced coloring} graph, is node partition each cluster nodes receives same information (color) from rest graph. In recent work we saw that networks such as gene regulatory networks, metabolic and neural organisms ranging bacteria to yeast humans are rich fibration related coloring. Networks based on real systems, however, built experimental data inherently incomplete, due missing links, collection errors, natural variations within specimens species. Therefore, it fair assume some existing were not detected our For reason, method find pseudosymmetries repair those when analyzing world networks. this paper introduce pseudobalanced \eqref{eq:mainip} problem, an integer programming formulation (a) calculates coloring taking into account data, (b) optimally repairs with minimal number added/removed edges maximize symmetry We apply C. elegans} connectome pseudocoloring optimal repair. Our solution compares well manually curated ground-truth solutions generated other methods link prediction.