Reciprocal regulation of genome topology and function is a fundamental and
enduring puzzle in biology. The wealth of data provided by Hi-C libraries offers
the opportunity to unravel this relationship. However, there is a need for a
comprehensive theoretical framework in order to extract topological information
for genome characterization and comparison. Here, we develop a toolbox for to-
pological analysis based on Circuit Topology, allowing for the quantification of in-
ter- and intracellular genomic heterogeneity, at various levels of fold complexity:
pairwise contact arrangement, higher-order contact arrangement, and topologi-
cal fractal dimension. Single-cell Hi-C data were analyzed and characterized based
on topological content, revealing not only a strong multiscale heterogeneity but
also highly conserved features such as a characteristic topological length scale
and topological signature motifs in the genome. We propose that these motifs
inform on the topological state of the nucleus and indicate the presence of active
loop extrusion.