Graph Neural Networks for Source Detection: A Review and Benchmark Study

TL;DR

The paper surveys Graph Neural Network (GNN) approaches for epidemic source detection on networks, clarifies problem settings (single-source vs multi-source) and data assumptions, and proposes a principled GNN architecture tailored to this task. Through extensive experiments on six static networks with SIR dynamics, the authors demonstrate that the proposed GNN substantially outperforms traditional methods (and probabilistic baselines like SME and MCMF) across key metrics, while showing robustness to moderate architectural choices. They analyze how detectability degrades with longer outbreak durations and how performance scales with training data, also examining the impact of uncertainty in the observation time T. A real-world case on the 2009 H1N1 pandemic illustrates practical applicability, and the work argues for epidemic-source detection as a benchmark task for evaluating GNN architectures, accompanied by public code and data for reproducibility.

Abstract

The source detection problem arises when an epidemic process unfolds over a contact network, and the objective is to identify its point of origin, i.e., the source node. Research on this problem began with the seminal work of Shah and Zaman in 2010, who formally defined it and introduced the notion of rumor centrality. With the emergence of Graph Neural Networks (GNNs), several studies have proposed GNN-based approaches to source detection. However, some of these works lack methodological clarity and/or are hard to reproduce. As a result, it remains unclear (to us, at least) whether GNNs truly outperform more traditional source detection methods across comparable settings. In this paper, we first review existing GNN-based methods for source detection, clearly outlining the specific settings each addresses and the models they employ. Building on this research, we propose a principled GNN architecture tailored to the source detection task. We also systematically investigate key questions surrounding this problem. Most importantly, we aim to provide a definitive assessment of how GNNs perform relative to other source detection methods. Our experiments show that GNNs substantially outperform all other methods we test across a variety of network types. Although we initially set out to challenge the notion of GNNs as a solution to source detection, our results instead demonstrate their remarkable effectiveness for this task. We discuss possible reasons for this strong performance. To ensure full reproducibility, we release all code and data on GitHub. Finally, we argue that epidemic source detection should serve as a benchmark task for evaluating GNN architectures.

Figures (11)

• Figure 1: Schematic representation of the source detection problem. An epidemic originates from node 1 and evolves over time. At observation time $t_1$ , a full snapshot of node states is available, but the identity of the source is unknown. The GNN receives as input the graph adjacency matrix and a node feature matrix containing the one-hot encoded epidemic states, and outputs a probability distribution over nodes indicating the most likely source.
• Figure 2: Proposed GNN model architecture. The four main components are enclosed in grey boxes. The numbers of preprocessing, message-passing, and postprocessing layers are tunable and may vary across datasets.
• Figure 3: Source detection performance across outbreak durations $T$. Each plot reports top-5 accuracy for our GNN architecture and for a baseline that selects the source uniformly at random from the infected subgraph. Bars indicate the average proportion of infectious and recovered nodes at each duration (secondary y-axis). In each plot, the fourth bar (marked by dotted lines) corresponds to the value of $T$ at which approximately 40% of all nodes are infected. Units of time are omitted, as the absolute values of durations are not relevant.
• Figure 4: Detection performance by outbreak size for the Karate network. The upper plot reports the top-5 accuracy of the different source detection methods across outbreak categories, defined by outbreak size. Error bars denote 95% confidence intervals. The lower plot depicts the absolute frequency of outbreaks within each category. The total number of outbreaks is $3{,}400$.
• Figure 5: Example outbreak scenario on the Karate network. The plot on the right depicts the network, with node colors indicating epidemic states (blue: susceptible, red: infectious, orange: recovered). The true source node (0) is emphasized by a larger size. The three bar plots on the left show the source predictions of the GNN (top), MCMF (middle), and SME (bottom). Nodes on the x-axis are ordered by descending GNN probabilities, and the true source is highlighted with a dark frame. Susceptible nodes are not included in the distributions.