Source detection is crucial for capturing the dynamics of real-world infectious diseases and informing effective containment strategies. Most existing approaches to source detection focus on conventional pairwise networks, whereas recent efforts on both mathematical modeling and analysis of contact data suggest that higher-order (e.g., group) interactions among individuals may both account for a large fraction of infection events and change our understanding of how epidemic spreading proceeds in empirical populations. In the present study, we propose a message-passing algorithm, called the HDMPN, for source detection for a stochastic susceptible-infectious dynamics on hypergraphs. By modulating the likelihood maximization method by the fraction of infectious neighbors, HDMPN aims to capture the influence of higher-order structures and do better than the conventional likelihood maximization. We numerically show that, in most cases, HDMPN outperforms benchmarks including the likelihood maximization method without modification.

Multilayer networked systems are ubiquitous in nature and engineering, and the robustness of these systems against failures is of great interest. A main line of theoretical pursuit has been percolation induced cascading failures, where interdependence between network layers is conveniently and tacitly assumed to be symmetric. In the real world, interdependent interactions are generally asymmetric. To uncover and quantify the impact of asymmetry in interdependence on network robustness, we focus on percolation dynamics in double-layer systems and implement the following failure mechanism: once a node in a network layer fails, the damage it can cause depends not only on its position in the layer but also on the position of its counterpart neighbor in the other layer. We find that the characteristics of the percolation transition depend on the degree of asymmetry, where the striking phenomenon of a switch in the nature of the phase transition from first- to second-order arises. We derive a theory to calculate the percolation transition points in both network layers, as well as the transition switching point, with strong numerical support from synthetic and empirical networks. Not only does our work shed light upon the factors that determine the robustness of multilayer networks against cascading failures, but it also provides a scenario by which the system can be designed or controlled to reach a desirable level of resilience.

Influential nodes in complex networks are typically defined as those nodes that maximize the asymptotic reach of a spreading process of interest. However, for practical applications such as viral marketing and online information spreading, one is often interested in maximizing the reach of the process in a short amount of time. The traditional definition of influencers in network-related studies from diverse research fields narrows down the focus to the late-time state of the spreading processes, leaving the following question unsolved: which nodes are able to initiate large-scale spreading processes, in a limited amount of time? Here, we find that there is a fundamental difference between the nodes -- which we call "fast influencers" -- that initiate the largest-reach processes in a short amount of time, and the traditional, "late-time" influencers. Stimulated by this observation, we provide an extensive benchmarking of centrality metrics with respect to their ability to identify both the fast and late-time influencers. We find that local network properties can be used to uncover the fast influencers. In particular, a parsimonious, local centrality metric (which we call social capital) achieves optimal or nearly-optimal performance in the fast influencer identification for all the analyzed empirical networks. Local metrics tend to be also competitive in the traditional, late-time influencer identification task.