Search

Temporal networks can naturally model real‐world complex phenomena such as contact networks, information dissemination and physical proximity. However, nodes and edges bear real‐time coordinates, making it difficult to organize them into discrete timeslices, without a loss of temporal information due to projection. Event‐based dynamic graph drawing rejects the notion of a timeslice and allows each node and edge to retain its own real‐valued time coordinate. While existing work has demonstrated clear advantages for this approach, they come at a running time cost. We investigate the problem of accelerating event‐based layout to make it more competitive with existing layout techniques. In this paper, we describe the design, implementation and experimental evaluation of MultiDynNoS, the first multi‐level event‐based graph layout algorithm. We consider three operators for coarsening and placement, inspired by Walshaw, GRIP and FM3, which we couple with an event‐based graph drawing algorithm. We also propose two extensions to the core algorithm: AutoTau and Bend Transfer. We perform two experiments: first, we compare MultiDynNoS variants to existing state‐of‐the‐art dynamic graph layout approaches; second, we investigate the impact of each of the proposed algorithm extensions. MultiDynNoS proves to be competitive with existing approaches, and the proposed extensions achieve their design goals and contribute in opening new research directions. [ABSTRACT FROM AUTHOR]

Abstract Writing in an academic context often requires students in higher education to acquire a new set of skills while familiarising themselves with the goals, objectives and requirements of the new learning environment. Students’ ability to continuously self-regulate their writing process, therefore, is seen as a determining factor in their learning success. In order to study students’ self-regulated learning (SRL) behaviour, research has increasingly been tapping into learning analytics (LA) methods in recent years, making use of multimodal trace data that can be obtained from students writing and working online. Nevertheless, little is still known about the ways students apply and govern SRL processes for academic writing online, and about how their SRL behaviour might change over time. To provide new perspectives on the use of LA approaches to examine SRL, this study applied a range of methods to investigate what they could tell us about the evolution of SRL tactics and strategies on a relational, co-temporal, contemporaneous and longitudinal level. The data originates from a case study in which a private Facebook group served as an online collaboration space in a first-year academic writing course for foreign language majors of English. The findings show that learners use a range of SRL tactics to manage their writing tasks and that different tactic can take up key positions in this process over time. Several shifts could be observed in students’ behaviour, from mainly addressing content-specific topics to more form-specific and social ones. Our results have also demonstrated that different methods can be used to study the relational, co-temporal, contemporaneous, and longitudinal dynamics of self-regulation in this regard, demonstrating the wealth of insights LA methods can bring to the table.

Many real-world systems can be expressed in temporal networks with nodes playing different roles in structure and function, and edges representing the relationships between nodes. Identifying critical nodes can help us control the spread of public opinions or epidemics, predict leading figures in academia, conduct advertisements for various commodities and so on. However, it is rather difficult to identify critical nodes, because the network structure changes over time in temporal networks. In this paper, considering the sequence topological information of temporal networks, a novel and effective learning framework based on the combination of special graph convolutional and long short-term memory network (LSTM) is proposed to identify nodes with the best spreading ability. The special graph convolutional network can embed nodes in each sequential weighted snapshot and LSTM is used to predict the future importance of timing-embedded features. The effectiveness of the approach is evaluated by a weighted Susceptible-Infected-Recovered model. Experimental results on four real-world temporal networks demonstrate that the proposed method outperforms both traditional and deep learning benchmark methods in terms of the Kendall τ coefficient and top k hit rate.

Periodicity is a frequently happening phenomenon for social interactions in temporal networks. Mining periodic communities are essential to understanding periodic group behaviors in temporal networks. Unfortunately, most previous studies for community mining in temporal networks ignore the periodic patterns of communities. In this paper, we study the problem of seeking periodic communities in a temporal network, where each edge is associated with a set of timestamps. We propose novel models, including $\sigma$ σ -periodic $k$ k -core and $\sigma$ σ -periodic $k$ k -clique, that represent periodic communities in temporal networks. Specifically, a $\sigma$ σ -periodic $k$ k -core (or $\sigma$ σ -periodic $k$ k -clique) is a $k$ k -core (or clique with size larger than $k$ k ) that appears at least $\sigma$ σ times periodically in the temporal graph. The problem of searching periodic core is efficient but the resulting communities may be not enough cohesive; the problem of enumerating all periodic cliques is not efficient (NP-hard) but the resulting communities are very cohesive. To compute all of them efficiently, we first develop two effective graph reduction techniques to significantly prune the temporal graph. Then, we transform the temporal graph into a static graph and prove that mining the periodic communities in the temporal graph equals mining communities in the transformed graph. Subsequently, we propose a decomposition algorithm to search maximal $\sigma$ σ -periodic $k$ k -core, a Bron-Kerbosch style algorithm to enumerate all maximal $\sigma$ σ -periodic $k$ k -cliques, and a branch-and-bound style algorithm to find the maximum $\sigma$ σ -periodic clique. The results of extensive experiments on five real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

Description of temporal networks and detection of dynamic communities have been hot topics of research for the last decade. However, no consensual answers to these challenges have been found due to the complexity of the task. Static communities are not well defined objects, and adding a temporal dimension makes the description even more difficult. In this article, we propose a coherent temporal clustering method to explore the dynamics of research communities: the Best Combination of Local Communities (BCLC). Our method aims at finding a good balance between two contradictory objectives: closely following the short-term evolution by finding optimal partitions at each time step, on the one hand, and temporal smoothing, which privileges historical continuity, on the other hand. We test our algorithm on two bibliographic data sets by comparing their mesoscale dynamic description to those derived from a (static) simple clustering algorithm applied over the whole data set. We show that our clustering algorithm can reveal more complex dynamics than the simple approach and reach a good agreement with expert's knowledge. [ABSTRACT FROM AUTHOR]

Real-world networks, such as phone-call networks and social networks, are often not static but temporal. Mining cohesive subgraphs from static graphs is a fundamental task in network analysis and has been widely investigated in the past decades. However, the concepts of cohesive subgraphs shift from static to temporal graphs raise many important problems. For instance, how to detect stable cohesive subgraphs on temporal networks such that the nodes in the subgraph are densely and stably connected over time. To address this problem, we resort to the conventional quasi-clique and propose a new model, called maximal $\rho $ -stable ($\delta, \gamma $)-quasi-clique, to capture both the cohesiveness and the stability of a subgraph. We show that the problem of enumerating all maximal $\rho $ -stable ($\delta, \gamma $)-quasi-cliques is NP-hard. To efficiently tackle our problem, we first devise a novel temporal graph reduction algorithm to significantly reduce the temporal graph without losing any maximal $\rho $ -stable ($\delta, \gamma $)-quasi-clique. Then, on the reduced temporal graph, we propose an effective branch and bound enumeration algorithm, named BB&SCM, with four carefully designed pruning techniques to accomplish the enumeration process. Finally, we conduct extensive experiments on seven real-world temporal graphs, and the results demonstrate that the temporal graph reduction algorithm can safely reduce 98% nodes of the temporal graph (with millions of nodes and edges) and BB&SCM is at least two orders of magnitude faster than the baseline algorithms. Moreover, we also evaluate the effectiveness of our model against other baseline models. [ABSTRACT FROM AUTHOR]

Abstract Temporal networks are graphs where each edge is associated with a timestamp denoting when two nodes interact. Temporal Subgraph Isomorphism (TSI) aims at retrieving all the subgraphs of a temporal network (called target) matching a smaller temporal network (called query), such that matched target edges appear in the same chronological order of corresponding query edges. Few algorithms have been proposed to solve the TSI problem (or variants of it) and most of them are applicable only to small or specific queries. In this paper we present TemporalRI, a new subgraph isomorphism algorithm for temporal networks with multiple contacts between nodes, which is inspired by RI algorithm. TemporalRI introduces the notion of temporal flows and uses them to filter the search space of candidate nodes for the matching. Our algorithm can handle queries of any size and any topology. Experiments on real networks of different sizes show that TemporalRI is very efficient compared to the state-of-the-art, especially for large queries and targets.

Abstract We study the problem of modeling temporal networks constrained by the size of a concurrent set, a characteristic of temporal networks shown to be important in many application areas, e.g., in transportation, social, process, and other networks. We propose a competition-driven model for the generation of such constrained networks. Our method carries out turns of competitions along the timeline where each node in a network is labeled with a probability to gain outgoing edges in competitions. We present a thorough theoretical analysis to investigate the cardinality and degree distributions of the generated networks. Our experimental results demonstrate that our model simulates real-world networks well and generates networks efficiently and at scale.

Abstract 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 lossless 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 single instances 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.

Abstract What do football passes and financial transactions have in common? Both are networked walk processes that we can observe, where records take the form of timestamped events that move something tangible from one node to another. Here we propose an approach to analyze this type of data that extracts the actual trajectories taken by the tangible items involved. The main advantage of analyzing the resulting trajectories compared to using, e.g., existing temporal network analysis techniques, is that sequential, temporal, and domain-specific aspects of the process are respected and retained. As a result, the approach lets us produce contextually-relevant insights. Demonstrating the usefulness of this technique, we consider passing play within association football matches (an unweighted process) and e-money transacted within a mobile money system (a weighted process). Proponents and providers of mobile money care to know how these systems are used—using trajectory extraction we find that 73% of e-money was used for stand-alone tasks and only 21.7% of account holders built up substantial savings at some point during a 6-month period. Coaches of football teams and sports analysts are interested in strategies of play that are advantageous. Trajectory extraction allows us to replicate classic results from sports science on data from the 2018 FIFA World Cup. Moreover, we are able to distinguish teams that consistently exhibited complex, multi-player dynamics of play during the 2017–2018 club season using ball passing trajectories, coincidentally identifying the winners of the five most competitive first-tier domestic leagues in Europe.

Abstract We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from this framework offers an improvement over existing pair-based models by moving away from edge-centric descriptions while keeping the description concise and relatively simple. For the contagion process, we consider the susceptible–infected–recovered (SIR) model, which is realized on a network with time-varying edges. We show that the shift in perspective from individual-based to pair-based quantities enables exact modelling of Markovian epidemic processes on temporal tree networks. On arbitrary networks, the proposed pair-based model provides a substantial increase in accuracy at a low computational and conceptual cost compared to the individual-based model. From the pair-based model, we analytically find the condition necessary for an epidemic to occur, otherwise known as the epidemic threshold. Due to the fact that the SIR model has only one stable fixed point, which is the global non-infected state, we identify an epidemic by looking at the initial stability of the model.

Abstract We study network centrality measures that take into account the specific structure of networks with time-stamped edges. In particular, we explore how such measures can be used to identify nodes most relevant for the spread of epidemics on directed, temporal contact networks. We present a percolation study on the French cattle trade network, proving that time-aware centrality measures such as the TempoRank significantly outperform measures defined on the static network. In order to make TempoRank amenable to large-scale networks, we show how it can be efficiently computed through direct simulation of time-respecting random walks.

Link temporality is a fundamental characteristic of diverse real networks across various domains, posing challenges in comprehending and controlling complex systems. The ultimate goal of understanding complex systems is to effectively manipulate them from their initial state to a desired state. Previous studies have predominantly focused on static networks due to computational complexity in analyzing temporal networks. In this study, we aim to enhance our understanding of link temporality and propose a graphical criterion for evaluating the dimension of controllable space in temporal systems by utilizing maximum matching in their aggregated static counterparts. This criterion overcomes the computation constraints associated with controlling large networks. We validated our graphical criterion in multiple temporal networks including model and real temporal networks, and observed that temporal networks with more degree-homogeneous snapshots are easier to be controlled. Moreover, we revealed that temporal process can disrupt the linear dependence of signals and found that the pivotal role of leaf links in expanding the dimension of controllable space in temporal networks. [ABSTRACT FROM AUTHOR]

In network analysis, real-world systems may be represented via graph models, where nodes and edges represent the set of biological objects (e.g., genes, proteins, molecules) and their interactions, respectively. This representative knowledge-graph model may also consider the dynamics involved in the evolution of the network (i.e., dynamic networks), in addition to a classic static representation (i.e., static networks). Bioinformatics solutions for network analysis allow knowledge extraction from the features related to a single network of interest or by comparing networks of different species. For instance, we may align a network related to a well known species to a more complex one in order to find a match able to support new hypotheses or studies. Therefore, the network alignment is crucial for transferring the knowledge between species, usually from simplest (e.g., rat) to more complex (e.g., human). Methods: In this paper, we present Dynamic Network Alignment based on Temporal Embedding (DANTE), a novel method for pairwise alignment of dynamic networks that applies the temporal embedding to investigate the topological similarities between the two input dynamic networks. The main idea of DANTE is to consider the evolution of interactions and the changes in network topology. Briefly, the proposed solution builds a similarity matrix by integrating the tensors computed via the embedding process and, subsequently, it aligns the pairs of nodes by performing its own iterative maximization function. Results: The performed experiments have reported promising results in terms of precision and accuracy, as well as good robustness as the number of nodes and time points increases. The proposed solution showed an optimal trade-off between sensitivity and specificity on the alignments produced on several noisy versions of the dynamic yeast network, by improving by ∼18.8% (with a maximum of 20.6%) the Area Under the Receiver Operating Characteristic (ROC) Curve (i.e., AUC or AUROC), compared to two well known methods: DYNAMAGNA++ and DYNAWAVE. From the point of view of quality, DANTE outperformed these by ∼91% as nodes increase and by ∼75% as the number of time points increases. Furthermore, a ∼23.73% improvement in terms of node correctness was reported with our solution on real dynamic networks.

As most of the community discovery methods are researched by static thought, some community discovery algorithms cannot represent the whole dynamic network change process efficiently. This paper proposes a novel dynamic community discovery method (Phylogenetic Planted Partition Model, PPPM) for phylogenetic evolution. Firstly, the time dimension is introduced into the typical migration partition model, and all states are treated as variables, and the observation equation is constructed. Secondly, this paper takes the observation equation of the whole dynamic social network as the constraint between variables and the error function. Then, the quadratic form of the error function is minimized. Thirdly, the Levenberg–Marquardt (L–M) method is used to calculate the gradient of the error function, and the iteration is carried out. Finally, simulation experiments are carried out under the experimental environment of artificial networks and real networks. The experimental results show that: compared with FaceNet, SBM + MLE, CLBM, and PisCES, the proposed PPPM model improves accuracy by 5% and 3%, respectively. It is proven that the proposed PPPM method is robust, reasonable, and effective. This method can also be applied to the general social networking community discovery field. [ABSTRACT FROM AUTHOR]

Abstract Epidemic spreading is a widely studied process due to its importance and possibly grave consequences for society. While the classical context of epidemic spreading refers to pathogens transmitted among humans or animals, it is straightforward to apply similar ideas to the spread of information (e.g., a rumor) or the spread of computer viruses. This paper addresses the question of how to optimally select nodes for monitoring in a network of timestamped contact events between individuals. We consider three optimization objectives: the detection likelihood, the time until detection, and the population that is affected by an outbreak. The optimization approach we use is based on a simple greedy approach and has been proposed in a seminal paper focusing on information spreading and water contamination. We extend this work to the setting of disease spreading and present its application with two example networks: a timestamped network of sexual contacts and a network of animal transports between farms. We apply the optimization procedure to a large set of outbreak scenarios that we generate with a susceptible-infectious-recovered model. We find that simple heuristic methods that select nodes with high degree or many contacts compare well in terms of outbreak detection performance with the (greedily) optimal set of nodes. Furthermore, we observe that nodes optimized on past periods may not be optimal for outbreak detection in future periods. However, seasonal effects may help in determining which past period generalizes well to some future period. Finally, we demonstrate that the detection performance depends on the simulation settings. In general, if we force the simulator to generate larger outbreaks, the detection performance will improve, as larger outbreaks tend to occur in the more connected part of the network where the top monitoring nodes are typically located. A natural progression of this work is to analyze how a representative set of outbreak scenarios can be generated, possibly taking into account more realistic propagation models.

Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only structural but also temporal patterns. However, as dynamic network literature stems from diverse fields and makes use of inconsistent terminology, it is challenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a lot of attention in recent years for their ability to perform well on a range of network science tasks, such as link prediction and node classification. Despite the popularity of graph neural networks and the proven benefits of dynamic network models, there has been little focus on graph neural networks for dynamic networks. To address the challenges resulting from the fact that this research crosses diverse fields as well as to survey dynamic graph neural networks, this work is split into two main parts. First, to address the ambiguity of the dynamic network terminology we establish a foundation of dynamic networks with consistent, detailed terminology and notation. Second, we present a comprehensive survey of dynamic graph neural network models using the proposed terminology.

A discrete-time deterministic epidemic model is proposed to better understand the contagious dynamics and the behaviour observed in the incidence of real infectious diseases. For this purpose, we analyse a SIRS model both in a random-mixing approach and in a small-world network formulation. The models include the basic parameters that characterize an epidemic: infection and recovery times, as well as mechanisms of contagion. Depending on the parameters, the random-mixing model has different types of behaviour of an epidemic: pathogen extinction; endemic infection; sustained oscillations and dynamic extinction. Spatial effects are included in our network-based approach, where each individual of a population is represented by a node of a small-world network. Our network-based approach includes rewiring connections to account for time-varying network structure, a consequence of the natural response to the emergence of an epidemic (e.g. avoiding contacts with infected individuals). Random and adaptive rewiring conditions are analysed and numerical simulation are made. A comparison of model predictions with the actual effects of COVID-19 infection on population that occurred in Italy and France is produced. Results of the time series of infected people show that our adaptive evolving networks represent effective strategies able to decrease the epidemic spreading.

Graph convolutional network (GCN) has made remarkable progress in learning good representations from graph-structured data. The layer-wise propagation rule of conventional GCN is designed in such a way that the feature aggregation at each node depends on the features of the one-hop neighbouring nodes. Adding an attention layer over the GCN can allow the network to provide different importance within various one-hop neighbours. These methods can capture the properties of static network, but is not well suited to capture the temporal patterns in time-varying networks. In this work, we propose a temporal graph attention network (TempGAN), where the aim is to learn representations from continuous-time temporal network by preserving the temporal proximity between nodes of the network. First, we perform a temporal walk over the network to generate a positive pointwise mutual information matrix (PPMI) which denote the temporal correlation between the nodes. Furthermore, we design a TempGAN architecture which uses both adjacency and PPMI information to generate node embeddings from temporal network. Finally, we conduct link prediction experiments by designing a TempGAN autoencoder to evaluate the quality of the embedding generated, and the results are compared with other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Temporal graphs are structures which model relational data between entities that change over time. Due to the complex structure of data, mining statistically significant temporal subgraphs, also known as temporal motifs, is a challenging task. In this work, we present an efficient technique for extracting temporal motifs in temporal networks. Our method is based on the novel notion of egocentric temporal neighborhoods, namely multi-layer structures centered on an ego node. Each temporal layer of the structure consists of the first-order neighborhood of the ego node, and corresponding nodes in sequential layers are connected by an edge. The strength of this approach lies in the possibility of encoding these structures into a unique bit vector, thus bypassing the problem of graph isomorphism in searching for temporal motifs. This allows our algorithm to mine substantially larger motifs with respect to alternative approaches. Furthermore, by bringing the focus on the temporal dynamics of the interactions of a specific node, our model allows to mine temporal motifs which are visibly interpretable. Experiments on a number of complex networks of social interactions confirm the advantage of the proposed approach over alternative non-egocentric solutions. The egocentric procedure is indeed more efficient in revealing similarities and discrepancies among different social environments, independently of the different technologies used to collect data, which instead affect standard non-egocentric measures. [ABSTRACT FROM AUTHOR]

Spatio-temporal evolution of soil moisture is a complex process and controlled by several factors including hydro-meteorological forcings. This study borrows a recently developed concept of temporal networks to capture the time-varying association between hydro-meteorological forcings and spatio-temporal evolution of soil moisture. Climate change and dynamic terrestrial environment cause slow but continuous change in the characteristics of hydro-meteorological forcings leading to variation in spatio-temporal distribution of soil moisture. Keeping this in the focus of the study, temporal networks based time-varying modelling framework is adapted for one-month to one-season (three-months) in advance prediction of monthly soil moisture for entire Indian mainland. Results indicate that the association among the hydro-meteorological forcings varies with both space and time. With the increase in prediction lead-time, the strength of association with the variables, such as pressure, wind and temperature, decreases and that with the variables like leaf area index remains informative. Among different seasons, the model shows superior performance for the monsoon and post monsoon periods. Next, the soil moisture based extremes are assessed by utilizing two deficit indices and two wetness indices. The model performance is highly satisfactory but varies over space and seasons, with a marginally better performance for the wetness indices. Overall, given the vast spatial extent of the Indian mainland, the proposed model performs robustly for almost all the climatic regions and may be promising for other parts of the world as well. [ABSTRACT FROM AUTHOR]

Cancer progression is dynamic, and tracking dynamic modules is promising for cancer diagnosis and therapy. Accumulated genomic data provide us an opportunity to investigate the underlying mechanisms of cancers. However, as far as we know, no algorithm has been designed for dynamic modules by integrating heterogeneous omics data. To address this issue, we propose an integrative framework for dynamic module detection based on regularized nonnegative matrix factorization method (DrNMF) by integrating the gene expression and protein interaction network. To remove the heterogeneity of genomic data, we divide the samples of expression profiles into groups to construct gene co-expression networks. To characterize the dynamics of modules, the temporal smoothness framework is adopted, in which the gene co-expression network at the previous stage and protein interaction network are incorporated into the objective function of DrNMF via regularization. The experimental results demonstrate that DrNMF is superior to state-of-the-art methods in terms of accuracy. For breast cancer data, the obtained dynamic modules are more enriched by the known pathways, and can be used to predict the stages of cancers and survival time of patients. The proposed model and algorithm provide an effective integrative analysis of heterogeneous genomic data for cancer progression. [ABSTRACT FROM AUTHOR]