The significance of the problem is hard to overstate. Misinformation about public health, elections, financial markets and disasters spreads through platforms whose underlying structures are enormous, interconnected graphs of users and their relationships. Once a rumor has propagated, forensic analysis of the pattern of infected or informed nodes offers clues about where the cascade began. Source detection formalizes this forensic task: given an observed snapshot of the spread, or a series of such snapshots over time, the goal is to infer the node or nodes most likely to have seeded the diffusion. The survey frames this as an inverse problem on a graph, and its central contribution is a rigorous classification of how different research communities have attacked that inversion.

At the foundations of the field lie diffusion models, mathematical descriptions of how information moves from node to node. The survey situates much of the classical literature within epidemic-style frameworks such as the susceptible-infected-recovered model and its variants, including the susceptible-exposed-infected-recovered formulation that introduces a latent period before a node becomes infectious. Work by Zhu and Ying on sample-path-based approaches in the SIR model, and by Zhou and colleagues on SEIR-based detection, exemplifies this tradition: the detector reasons backward from the observed infection pattern through the stochastic dynamics of the spread model to assign a likelihood to each candidate source. Shah and Zaman’s foundational result, which introduced a rumor centrality measure and established diffusion-based source estimators on tree-structured networks, remains a touchstone that the survey returns to repeatedly.

Centrality-based methods form the first major methodological family examined in the review. These techniques treat the source as the node that best explains the observed structure of the rumor-spreading subgraph, ranking candidates by measures such as degree, closeness, betweenness or specialized scores like rumor centrality and eigenvalue-based spectral techniques. Comin and da Fontoura Costa’s approach of identifying the starting point of a spreading process through network centrality, and Fioriti and Chinnici’s spectral method, are highlighted as representative examples. The appeal of these methods is computational simplicity and interpretability; their weakness is that they often presuppose idealized network topologies, such as trees or regular graphs, and can degrade sharply on the irregular, clustered, small-world topologies that characterize real social media. The survey is careful to catalog these assumptions, drawing on classic network models including Erdős-Rényi random graphs, Watts-Strogatz small-world networks and star graph structures that recur throughout the theoretical literature.

Beyond simple centrality, the survey traces a progression toward probabilistic and Bayesian estimators. Maximum a posteriori and maximum likelihood formulations, such as those developed by Chang and colleagues and by Spencer and Srikant for star networks, recast source identification as statistical inference over candidate nodes. Message-passing approaches, exemplified by Lokhov and co-workers’ dynamic message-passing algorithm, approximate otherwise intractable posterior distributions on loopy graphs. The review also covers the growing body of work on harder situational variants: sources with different start times, as treated by Ji, Tay and Varshney; rumors spreading on time-varying topologies, as studied by Jiang and colleagues; detectors operating under probabilistic sampling or partial observations, following Karamchandani, Alexandru and Dragotti, and Zhang and colleagues; and adversarial settings in which queried users return untruthful answers, a scenario examined by Choi and collaborators. Each variant, the survey argues, changes the problem’s difficulty in ways that demand tailored estimators rather than off-the-shelf adaptations.

A second axis of classification concerns the number of sources. Early work largely assumed a single culprit, but real misinformation campaigns often involve multiple coordinated origins. Prakash, Vreeken and Faloutsos posed the problem directly, asking how many culprits an epidemic contains and which ones they are, while Wang, Dong, Zhang and Tan demonstrated the value of diversity from multiple observations for rooting out rumor sources. The survey collects approaches to multi-source detection under partial observability, including combinatorial optimization formulations by Zhang, Xu, Wu and Du, and methods that exploit community structure and monitor stations, such as the greedy monitoring selection of Jin and colleagues and the community-and-monitor-informed identification of Devarapalli, Das and Biswas. The review also emphasizes interconnected and overlapping network settings, where rumors jump between coupled platforms, complicating the notion of a single underlying graph.

The most technologically current portion of the survey addresses machine learning, and in particular graph neural networks and deep generative models. Dong, Zheng and colleagues introduced graph convolutional networks for multiple rumor source detection, treating the task as learning over the observed diffusion subgraph rather than hand-designing a likelihood. Wang, Jiang and Zhao proposed an invertible graph diffusion neural network for source localization, and Ling and colleagues framed graph diffusion source localization as a graph inverse problem solvable with variational autoencoders. Denoising diffusion models, which generate samples through iterative denoising, have been adapted to the inverse problem, notably in the two-stage denoising diffusion approach of Huang and co-workers. GIN-SD, introduced by Cheng, Zhu and colleagues, tackles source detection in graphs with incomplete nodes using positional encoding and attentive fusion, addressing the pervasive problem of missing data. The survey’s authors themselves contribute context from their prior work on class-balanced embedding networks that address graph node imbalance in social media rumor source detection, a practical concern because true sources are vanishingly rare compared with the mass of infected nodes.

Practical deployment, the review stresses, hinges on scalability and data. Exact Bayesian inference on million-node graphs is computationally prohibitive, so the survey compares the computational overhead of each method and catalogs approximation techniques, including random-walk-based identification, distributed inference via boosted federated learning as proposed by Wang and colleagues, and label-propagation-style heuristics descended from work by Zhu and Ghahramani. On the data side, the survey assembles a comprehensive inventory of benchmark resources, spanning synthetic networks generated from random graph models and canonical real datasets: the PHEME dataset of rumors and non-rumors, Stanford Large Network Dataset Collection graphs, Facebook ego networks, the Enron email corpus, reality mining data, meme-tracker traces, wiki-vote signed networks, college messaging networks and epidemic records such as influenza A H1N1 school outbreak data. This compilation alone makes the review a practical reference for researchers designing experiments, since inconsistent benchmarks have historically made head-to-head comparison of source detection methods difficult.

Equally important is the survey’s treatment of evaluation metrics, the yardsticks by which detection success is measured, and its frank assessment of open challenges. The authors, who contributed equally and whose work is supported by India’s Rashtriya Uchchatar Shiksha Abhiyan 2.0 program, note that performance depends critically on observation type, timing, topology knowledge and the realism of the assumed propagation model, and that metrics reported in the literature vary widely, complicating claims of superiority. Their analysis of these validation practices points toward a future research agenda: models that tolerate incomplete and noisy observations, architectures that scale to platform-sized graphs, methods robust to coordinated multi-source campaigns and adaptive diffusion strategies, and integration with adjacent challenges such as deepfake detection and image provenance analysis, both of which appear among the cited frontier works. As social platforms confront regulatory pressure to limit harmful misinformation, the ability to trace a rumor to its origin is shifting from an academic curiosity to an operational necessity, and this survey provides the most complete map yet of the technical terrain that such tracing will have to cross.

Subject of Research: Rumor source detection methodologies in social networks

Article Title: State of the art in rumor source detection: an in-depth survey

Article References: Gopal, G. N., & Kovoor, B. C. (2026). State of the art in rumor source detection: an in-depth survey. International Journal of Data Science and Analytics, 22(1), Article 296. https://doi.org/10.1007/s41060-026-01269-5

Image Credits: AI Generated

DOI: 10.1007/s41060-026-01269-5

Keywords: rumor source detection, social networks, centrality measures, diffusion models, graph neural networks, deep generative models, misinformation, SIR model, multiple source detection, scalability, benchmark datasets, survey