Higher-order architecture of metastatic networks: A statistical mechanics approach via validated hypergraphs

Metastasis is a complex, stochastic systemic process characterized by non-random spread patterns to secondary organs. Conventional dyadic projections fragment multi-organ interactions into independent events, effectively discarding irreducible higher-order topological information and the synergistic nature of clonal dissemination. This limitation often leads to conflating first-order topological properties with intrinsic biological affinities, particularly in the absence of validation against structure-aware null models. To address this methodological gap, we present a higher-order hypergraph framework that preserves simultaneous colonization patterns and accounts for emergent architectures that cannot be reduced to simple pairwise interactions. Our approach incorporates: (1) a functional partition of the network nodes ( V S , V T ) to distinguish organs with documented reseeding capacity; and (2) a directed association matrix S quantifying the non-linear information flux and dependencies among source organs. We implement a rigorous validation protocol by exploring the constrained null-space of the metastatic hypergraph using a Metropolis–Hastings MCMC algorithm. By contrasting the empirical data against a degree-preserving Canonical Ensemble (Configuration Model), this framework acts as a structural filter, demonstrating that many observed metastatic hotspots are spurious correlations emergent from nodal degree heterogeneity rather than genuine biological co-selection. By de-convoluting effective affinities from degree-driven effects, our method identifies a robust structural backbone that remains invariant under topological perturbations. This work shifts the focus from counting isolated events to quantifying the statistical mechanics of non-linear disease progression in complex biological networks.