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Register a new userUniversal nonlinear infection kernel from heterogeneous exposure on higher-order networks
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The colocation of individuals in different environments is an important prerequisite for exposure to infectious diseases on a social network. Standard epidemic models fail to capture the potential complexity of this scenario by (1) neglecting the higher-order structure of contacts which typically occur through environments like workplaces, restaurants, and households; and by (2) assuming a linear relationship between the exposure to infected contacts and the risk of infection. Here, we leverage a hypergraph model to embrace the heterogeneity of environments and the heterogeneity of individual participation in these environments. We find that combining heterogeneous exposure with the concept of minimal infective dose induces a universal nonlinear relationship between infected contacts and infection risk. Under nonlinear infection kernels, conventional epidemic wisdom breaks down with the emergence of discontinuous transitions, super-exponential spread, and hysteresis.
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Simple models of infectious diseases tend to assume random mixing of individuals, but real interactions are not random pairwise encounters: they occur within various types of gatherings such as workplaces, households, schools, and concerts, best described by a higher-order network structure. We model contagions on higher-order networks using group-based approximate master equations, in which we track all states and interactions within a group of nodes and assume a mean-field coupling between them. Using the Susceptible-Infected-Susceptible dynamics, our approach reveals the existence of a mesoscopic localization regime, where a disease can concentrate and self-sustain only around large groups in the network overall organization. In this regime, the phase transition is smeared, characterized by an inhomogeneous activation of the groups. At the mesoscopic level, we observe that the distribution of infected nodes within groups of a same size can be very dispersed, even bimodal. When considering heterogeneous networks, both at the level of nodes and groups, we characterize analytically the region associated with mesoscopic localization in the structural parameter space. We put in perspective this phenomenon with eigenvector localization and discuss how a focus on higher-order structures is needed to discern the more subtle localization at the mesoscopic level. Finally, we discuss how mesoscopic localization affects the response to structural interventions and how this framework could provide important insights for a broad range of dynamics.
Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly describe social contagion, where individuals acquire new norms or ideas after simultaneous exposure to multiple sources of infections. Simplicial contagion has been proposed as an alternative framework where simplices are used to encode group interactions of any order. The presence of higher-order interactions leads to explosive epidemic transitions and bistability which cannot be obtained when only dyadic ties are considered. In particular, critical mass effects can emerge even for infectivity values below the standard pairwise epidemic threshold, where the size of the initial seed of infectious nodes determines whether the system would eventually fall in the endemic or the healthy state. Here we extend simplicial contagion to time-varying networks, where pairwise and higher-order simplices can be created or destroyed over time. By following a microscopic Markov chain approach, we find that the same seed of infectious nodes might or might not lead to an endemic stationary state, depending on the temporal properties of the underlying network structure, and show that persistent temporal interactions anticipate the onset of the endemic state in finite-size systems. We characterize this behavior on higher-order networks with a prescribed temporal correlation between consecutive interactions and on heterogeneous simplicial complexes, showing that temporality again limits the effect of higher-order spreading, but in a less pronounced way than for homogeneous structures. Our work suggests the importance of incorporating temporality, a realistic feature of many real-world systems, into the investigation of dynamical processes beyond pairwise interactions.
Graph neural networks (GNNs) have been widely used in deep learning on graphs. They can learn effective node representations that achieve superior performances in graph analysis tasks such as node classification and node clustering. However, most methods ignore the heterogeneity in real-world graphs. Methods designed for heterogeneous graphs, on the other hand, fail to learn complex semantic representations because they only use meta-paths instead of meta-graphs. Furthermore, they cannot fully capture the content-based correlations between nodes, as they either do not use the self-attention mechanism or only use it to consider the immediate neighbors of each node, ignoring the higher-order neighbors. We propose a novel Higher-order Attribute-Enhancing (HAE) framework that enhances node embedding in a layer-by-layer manner. Under the HAE framework, we propose a Higher-order Attribute-Enhancing Graph Neural Network (HAEGNN) for heterogeneous network representation learning. HAEGNN simultaneously incorporates meta-paths and meta-graphs for rich, heterogeneous semantics, and leverages the self-attention mechanism to explore content-based nodes interactions. The unique higher-order architecture of HAEGNN allows examining the first-order as well as higher-order neighborhoods. Moreover, HAEGNN shows good explainability as it learns the importances of different meta-paths and meta-graphs. HAEGNN is also memory-efficient, for it avoids per meta-path based matrix calculation. Experimental results not only show HAEGNN superior performance against the state-of-the-art methods in node classification, node clustering, and visualization, but also demonstrate its superiorities in terms of memory efficiency and explainability.
Identifying the most influential nodes in networked systems is vital to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards higher-order networks has rendered them void of performance guarantees. We propose a new measure of nodes centrality, which is no longer a scalar value, but a vector with dimension one lower than the highest order of interaction in the graph. Such a vectorial measure is linked to the eigenvector centrality for networks containing only pairwise interactions, whereas it has a significant added value in all other situations where interactions occur at higher-orders. In particular, it is able to unveil different roles which may be played by a same node at different orders of interactions, an information which is impossible to be retrieved by single scalar measures.
An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche shapes, i.e., the temporal profiles that characterize the growth and decay of avalanches of fixed duration. At the critical point of the dynamics the average avalanche shapes for different durations can be rescaled so that they collapse onto a single universal curve. We apply Markov branching process theory to derive a simple equation governing the average avalanche shape for cascade dynamics on networks. Analysis of the equation at criticality demonstrates that nonsymmetric average avalanche shapes (as observed in some experiments) occur for certain combinations of dynamics and network topology; specifically, on networks with heavy-tailed degree distributions. We give examples using numerical simulations of models for information spreading, neural dynamics, and behaviour adoption and we propose simple experimental tests to quantify whether cascading systems are in the critical state.
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