A novel framework for network null models: bridging optimal transport theory and complex networks

Abstract This paper introduces a novel Optimal Transport–based framework for generating null models of complex networks. The method provides a canonical maximum-entropy ensemble that preserves selected node-level properties while maintaining controlled randomness elsewhere. The node-level in- and out-strength sequences are enforced in expectation through marginal constraints on the transport coupling, whereas additional structural tendencies, such as degree-related biases, are incorporated flexibly through the design of a cost matrix. This allows the model to reproduce degree patterns and other features statistically as a soft bias, without enforcing them as formal constraints. The approach is computationally efficient, relying on an entropy-regularized Optimal Transport problem solved via a Sinkhorn-type iterative procedure, and supports the generation of random network realizations by sampling from the resulting coupling. Experiments on synthetic data demonstrate that the model faithfully preserves in- and out-strength sequences in expectation and accurately reproduces network properties induced by the cost structure. An application to the International Trade Network shows how the methodology allows to distinguish between patterns attributable to basic connectivity constraints and those reflecting genuine higher-order organization.