We consider the problem of identifying the source of a rumor in a network, given only a snapshot observation of infected nodes after the rumor has spread. Classical approaches, such as the maximum likelihood (ML) and joint maximum likelihood (JML) estimators based on the conventional Susceptible–Infectious (SI) model, exhibit degeneracy, failing to uniquely identify the source even in simple network structures. To address these limitations, we propose a generalized estimator that incorporates independent random observation times. To capture the structure of information flow beyond graphs, our formulations consider rate constraints on the rumor and the multicast capacities for cyclic polylinking networks. Furthermore, we develop forward elimination and backward search algorithms for rate-constrained source detection and validate their effectiveness and scalability through comprehensive simulations. Our study establishes a rigorous and scalable foundation on the infodemic source detection.

Source identification is constrained not only by network connectivity but also by whether a finite message can reach observed nodes before a deadline. We study deterministic source-candidate elimination in directed networks with arc capacities and transit times. A time-expanded construction gives an exact causal network-coding characterization in which a candidate is retained if and only if its temporal min-cut to every required recipient is at least the message size. Rejection is therefore conservative for any weaker compliant routing or replication protocol. We derive an equivalent minimum-cost circulation computation, monotone certificates under parameter uncertainty, and closed-form formulas for bidirected trees, including linear-time evaluation for uniform capacities and an $O\left(\right|V\left|{\log }^2\right|V\left|\right)$ centroid decomposition algorithm for heterogeneous capacities. Protocol-generated experiments show zero true-source eliminations and substantial refinement in routing regimes. Held-out calibration supports transfer to unseen networks. On benchmark representations of 40 real backbone topology families with 50 to 197 nodes, mean candidate retention falls from 99.3% under static screening to 25.3% under exact temporal screening, without true-source elimination. A focused RLNC diagnostic attributes weak refinement in coding-rich regimes to the static screen retaining all candidates and to broad temporal feasibility, while decode-before-forward restrictions create a substantially larger protocol gap.