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Network embedding techniques are powerful to capture structural regularities in networks and to identify similarities between their local fabrics. However, conventional network embedding models are developed for static structures, commonly consider nodes only and they are seriously challenged when the network is varying in time. Temporal networks may provide an advantage in the description of real systems, but they code more complex information, which could be effectively represented only by a handful of methods so far. Here, we propose a new method of event embedding of temporal networks, called weg2vec, which builds on temporal and structural similarities of events to learn a low dimensional representation of a temporal network. This projection successfully captures latent structures and similarities between events involving different nodes at different times and provides ways to predict the final outcome of spreading processes unfolding on the temporal structure.
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Low-dimensional vector representations of network nodes have proven successful to feed graph data to machine learning algorithms and to improve performance across diverse tasks. Most of the embedding techniques, however, have been developed with the goal of achieving dense, low-dimensional encoding of network structure and patterns. Here, we present a node embedding technique aimed at providing low-dimensional feature vectors that are informative of dynamical processes occurring over temporal networks -- rather than of the network structure itself -- with the goal of enabling prediction tasks related to the evolution and outcome of these processes. We achieve this by using a modified supra-adjacency representation of temporal networks and building on standard embedding techniques for static graphs based on random-walks. We show that the resulting embedding vectors are useful for prediction tasks related to paradigmatic dynamical processes, namely epidemic spreading over empirical temporal networks. In particular, we illustrate the performance of our approach for the prediction of nodes epidemic states in a single instance of a spreading process. We show how framing this task as a supervised multi-label classification task on the embedding vectors allows us to estimate the temporal evolution of the entire system from a partial sampling of nodes at random times, with potential impact for nowcasting infectious disease dynamics.
The analysis of temporal networks has a wide area of applications in a world of technological advances. An important aspect of temporal network analysis is the discovery of community structures. Real data networks are often very large and the communities are observed to have a hierarchical structure referred to as multi-scale communities. Changes in the community structure over time might take place either at one scale or across all scales of the community structure. The multilayer formulation of the modularity maximization (MM) method introduced captures the changing multi-scale community structure of temporal networks. This method introduces a coupling between communities in neighboring time layers by allowing inter-layer connections, while different values of the resolution parameter enable the detection of multi-scale communities. However, the range of this parameters values must be manually selected. When dealing with real life data, communities at one or more scales can go undiscovered if appropriate parameter ranges are not selected. A novel Temporal Multi-scale Community Detection (TMSCD) method overcomes the obstacles mentioned above. This is achieved by using the spectral properties of the temporal network represented as a multilayer network. In this framework we select automatically the range of relevant scales within which multi-scale community partitions are sought.
Most previous studies of epidemic dynamics on complex networks suppose that the disease will eventually stabilize at either a disease-free state or an endemic one. In reality, however, some epidemics always exhibit sporadic and recurrent behaviour in one region because of the invasion from an endemic population elsewhere. In this paper we address this issue and study a susceptible-infected-susceptible epidemiological model on a network consisting of two communities, where the disease is endemic in one community but alternates between outbreaks and extinctions in the other. We provide a detailed characterization of the temporal dynamics of epidemic patterns in the latter community. In particular, we investigate the time duration of both outbreak and extinction, and the time interval between two consecutive inter-community infections, as well as their frequency distributions. Based on the mean-field theory, we theoretically analyze these three timescales and their dependence on the average node degree of each community, the transmission parameters, and the number of intercommunity links, which are in good agreement with simulations, except when the probability of overlaps between successive outbreaks is too large. These findings aid us in better understanding the bursty nature of disease spreading in a local community, and thereby suggesting effective time-dependent control strategies.
Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks, little work has been devoted to the understanding of how such heterogeneities can emerge from microscopic mechanisms at the level of nodes and links. Here we show that long-term memory effects are present in the creation and disappearance of links in empirical networks. We thus consider a simple generative modeling framework for temporal networks able to incorporate these memory mechanisms. This allows us to study separately the role of each of these mechanisms in the emergence of heterogeneous network dynamics. In particular, we show analytically and numerically how heterogeneous distributions of contact durations, of inter-contact durations and of numbers of contacts per link emerge. We also study the individual effect of heterogeneities on dynamical processes, such as the paradigmatic Susceptible-Infected epidemic spreading model. Our results confirm in particular the crucial role of the distributions of inter-contact durations and of the numbers of contacts per link.
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that interactions are more likely to occur between individuals with similar ranks. It provides a natural statistical significance test for the inferred hierarchy, and it can be used to perform inference tasks such as predicting the existence or direction of edges. The ranking is obtained by solving a linear system of equations, which is sparse if the network is; thus the resulting algorithm is extremely efficient and scalable. We illustrate these findings by analyzing real and synthetic data, including datasets from animal behavior, faculty hiring, social support networks, and sports tournaments. We show that our method often outperforms a variety of others, in both speed and accuracy, in recovering the underlying ranks and predicting edge directions.
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