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The use of quantum satellites can be significant paving the way for novel telecommunications network paradigms, making it possible to connect remote regions. Given the rapid development of quantum communication technologies, many studies are focusing on quantum satellites interconnections via Free Space Optic (FSO), especially considering that the adoption of wired alternatives did not achieve significant results, mainly in terms of covering long distances. In this context, the global interconnection of Quantum Computers (QCs) through the so-called Quantum Internet (QI) compels for new communications and computing architectures such as Quantum Cloud (QCloud). To this purpose, the deployment of Satellite Quantum Networks (SQNs) could make easily available innovative services spanning from security to advanced computing, especially by using Software-Defined Networking (SDN) technology, which is considered a significant enabler for the management of SQNs. Moreover, considering the rapid variability of the topology in terms of nodes and links features, the paper proposes a specific Temporal Networks (TNs) optimization strategy embedded in an SDN Controller ecosystem, dynamically optimizing the path durations to achieve the highest entanglement rate, while limiting the disconnections. Performance evaluation in a worst case scenario shows that the proposed framework is able to support distributed applications by exploiting all the connection opportunities.

Representing the nodes of continuous-time temporal graphs in a low-dimensional latent space has wide-ranging applications, from prediction to visualization. Yet, analyzing continuous-time relational data with timestamped interactions introduces unique challenges due to its sparsity. Merely embedding nodes as trajectories in the latent space overlooks this sparsity. However, a natural way to account for this sparsity is to model the uncertainty around the latent positions. In this paper, we propose TGNE (Temporal Gaussian Network Embedding), an innovative method that bridges two distinct strands of literature: the statistical analysis of networks via Latent Space Models (LSM) and temporal graph machine learning. TGNE embeds nodes as piece-wise linear trajectories of Gaussian distributions in the latent space, capturing both structural information and uncertainty around the trajectories. We evaluate TGNE’s effectiveness in reconstructing the original graph and modelling uncertainty. The results demonstrate that TGNE generates time-varying embedding locations that can accurately reconstruct missing parts of the network based on observed ones. Furthermore, the uncertainty estimates align experimentally with the time-varying degree distribution in the network, providing valuable insights into the temporal dynamics of the graph. To facilitate reproducibility, we provide an open-source implementation of TGNE at https://github.com/aida-ugent/tgne/.

One of the key goals of Informetrics is to identify citation-based popular articles among so many other aspects, such as determining popular research topics, identifying influential scholars, and predicting hot trends in science. These can be achieved by applying network science approaches to scientific networks and formulating the problem as a popular (most-cited) node ranking task. To rank the papers based on their future citation gain. In this work a deep learning based framework is proposed. Which helps in automatic node level feature extraction and can make node level prediction in dynamic graphs such as citation networks. To achieve this we have learned global ranking preserve d dimensional node embedding. We have only considered temporal features, which makes it suitable for generalisation to other networks. Although our model can consider node level explicit features also. Further we have given novel cost function which can be easily solve ranking problem for dynamic graphs using probabilistic regression method. Which can be easily optimised. Another novelty of our work is that our model can be trained using different snapshots of the graph and different time. Further trained model can be used to make future prediction. The proposed model has been tested on an arXiv paper citation network using six standard information retrieval-based metrics. The results show that our proposed model outperforms, on average, other state-of-the-art static models as well as dynamic node ranking models. The outcome of this research study leads to informed data-driven decision-making in science, such as the allocation and distribution of research funds and investment in strategic research centers. When considering past time window size as 10 months and making prediction after 10 months our proposed model’s performance on various ranking based evaluation metrics are as follows: AUC-0.974, Kendal’s rank correlation tau-0.455, Precision- 0.643, Novelty-0.0456, Temporal novelty-0.375 and on NDCG-0.949. Our model is able to make long term trend prediction with just training on short time window.

Graph neural networks (GNNs) are rapidly becoming the dominant way to learn on graph-structured data. Link prediction is a near-universal benchmark for new GNN models. Many advanced models such as Dynamic graph neural networks (DGNNs) specifically target dynamic graphs. However, these models, particularly DGNNs, are rarely compared to each other or existing heuristics. Different works evaluate their models in different ways, thus one cannot compare evaluation metrics and their results directly. Motivated by this, we perform a comprehensive comparison study. We compare link prediction heuristics, GNNs, discrete DGNNs, and continuous DGNNs on the dynamic link prediction task. In total we summarize the results of over 3200 experimental runs ( $\approx 1.5$ years of computation time). We find that simple link prediction heuristics perform better than GNNs and DGNNs, different sliding window sizes greatly affect performance, and of all examined graph neural networks, that DGNNs consistently outperform static GNNs. This work is a continuation of our previous work, a foundation of dynamic networks and theoretical review of DGNNs. In combination with our survey, we provide both a theoretical and empirical comparison of DGNNs.

Mobility is a critical element for understanding human contact networks. In many studies, the researchers use random processes to model human mobility. However, people do not move randomly in their environment. Their interactions do not depend only on spatial constraints but on their temporal, social, economic, and cultural activities. The topological structure of the physical and/or proximity contact networks depends, therefore, entirely on the mobility patterns. This paper performs an extensive comparative analysis of real-world temporal contact networks and synthetic networks based on influential mobility models. Results show that the various topological properties of most of the synthetic datasets depart from those observed in real-world contact networks because the randomness of some mobility parameters tends to move away from human contact properties. However, it appears that data generated using Spatio-Temporal Parametric Stepping (STEPS) mobility model reveals similarities with real temporal contact networks such as heavy-tailed distribution of contact duration, frequency of pairs of contacts, and the bursty phenomenon. These results pave the way for further improvement of mobility models to generate meaningful artificial contact networks.

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]

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]

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.

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]

The spread of influence in networks is a topic of great importance in many application areas. For instance, one would like to maximise the coverage, limiting the budget for marketing campaign initialisation and use the potential of social influence. To tackle this and similar challenges, more than a decade ago, researchers started to investigate the influence maximisation problem. The challenge is to find the best set of initially activated seed nodes in order to maximise the influence spread in networks. In typical approach we will activate all seeds in single stage, at the beginning of the process, while in this work we introduce and evaluate a new approach for seeds activation in temporal networks based on sequential seeding. Instead of activating all nodes at the same time, this method distributes the activations of seeds, leading to higher ranges of influence spread. The results of experiments performed using real and randomised networks demonstrate that the proposed method outperforms single stage seeding in 71% of cases by nearly 6% on average. Knowing that temporal networks are an adequate choice for modelling dynamic processes, the results of this work can be interpreted as encouraging to apply temporal sequential seeding for real world cases, especially knowing that more sophisticated seed selection strategies can be implemented by using the seed activation strategy introduced in this work.

This article presents the implementation in real devices of the consensus-based routing algorithm (CRA). The CRA has the advantage of basing the route calculation on an availability function, considering the local conditions of a delimited neighborhood. This attribute allows the best candidate to be chosen to establish a connection within the temporary network.Previously, simulations of the operation of the presented algorithm have been shown, this article shows its performance in a physical environment, using open hardware. In this way, real measures of communication latency between devices and task scheduling are considered. The characteristics as mentioned earlier make the CRA a good option to apply in temporal networks since they are present for brief moments, so they do not require the route to be two-way. [ABSTRACT FROM AUTHOR]

Centrality of nodes is very useful for understanding the behavior of systems and has recently attracted plenty of attention from researchers. In this paper, we propose a new eigenvector centrality based on node similarity for ranking nodes in multilayer and temporal networks under the framework of tensor computation, referred to as the ECMSim. We define a fourth-order tensor to represent the multilayer and temporal networks. The relationships between different layers(or time stamps) can be depicted by using node similarity. Based on the defined tensor, we establish the tensor equation to obtain nodes centrality values. The nodes centrality values also can be viewed as the Perron eigenvector of a multi-homogeneous map. Furthermore, we show the existence and uniqueness of the proposed centrality measure by existing results. Numerical experiments are carried out to demonstrate that the proposed centrality outperforms some existing ranking methods.

Many complex systems can be modeled as temporal networks with time-evolving connections. The influence of their characteristics on epidemic spreading is analyzed in a susceptible-infected-susceptible epidemic model illustrated by the discrete-time Markov chain approach. We develop the analytical epidemic thresholds in terms of the spectral radius of weighted adjacency matrix by averaging temporal networks, e.g., periodic, nonperiodic Markovian networks, and a special nonperiodic non-Markovian network (the link activation network) in time. We discuss the impacts of statistical characteristics, e.g., bursts and duration heterogeneity, as well as time-reversed characteristic on epidemic thresholds. We confirm the tightness of the proposed epidemic thresholds with numerical simulations on seven artificial and empirical temporal networks and show that the epidemic threshold of our theory is more precise than those of previous studies. [ABSTRACT FROM AUTHOR]

Dense subgraph discovery has proven useful in various applications of temporal networks. We focus on a special class of temporal networks whose nodes and edges are kept fixed, but edge weights regularly vary with timestamps. However, finding dense subgraphs in temporal networks is non-trivial, and its state of the art solution uses a filter-and-verification framework that is not scalable on large temporal networks. In this study, we propose a highly efficient approach to finding dense subgraphs in large temporal networks with $T$ T timestamps. (1) We first develop a statistics-driven approach that employs hidden statistics to identifying $k$ k time intervals, instead of $T(T+1)/2$ T (T + 1) / 2 ones ($k$ k is typically much smaller than $T$ T ), which strikes a balance between quality and efficiency. (2) After proving that the problem has no constant factor approximation algorithms, we design better heuristic algorithms to attack the problem, by connecting finding dense subgraphs with a variant of the Prize Collecting Steiner Tree problem. (3) Finally, we have conducted an extensive experimental study to verify that our approach is both effective and efficient. [ABSTRACT FROM AUTHOR]

ChronoGraph is a novel system enabling temporal graph traversals. Compared to snapshot-oriented systems, this traversal-oriented system is suitable for analyzing information diffusion over time without violating a time constraint on temporal paths. The cornerstone of ChronoGraph aims at bridging the chasm between point-based semantics and period-based semantics and the gap between temporal graph traversals and static graph traversals. Therefore, our graph model and traversal language provide the temporal syntax for both semantics, and we present a method converting point-based semantics to period-based ones. Also, ChronoGraph exploits the temporal support and parallelism to handle the temporal degree, which explosively increases compared to static graphs. We demonstrate how three traversal recipes can be implemented on top of our system: temporal breadth-first search (tBFS), temporal depth-first search (tDFS), and temporal single source shortest path (tSSSP). According to our evaluation, our temporal support and parallelism enhance temporal graph traversals in terms of convenience and efficiency. Also, ChronoGraph outperforms existing property graph databases in terms of temporal graph traversals. We prototype ChronoGraph by extending Tinkerpop, a de facto standard for property graphs. Therefore, we expect that our system would be readily accessible to existing property graph users. [ABSTRACT FROM AUTHOR]

Modern networks are very large in size and also evolve with time. As their sizes grow, the complexity of performing network analysis grows as well. Getting a smaller representation of a temporal network with similar properties will help in various data mining tasks. In this paper, we study the novel problem of getting a smaller diffusion-equivalent representation of a set of time-evolving networks. We first formulate a well-founded and general temporal-network condensation problem based on the so-called system-matrix of the network. We then propose NetCondense, a scalable and effective algorithm which solves this problem using careful transformations in sub-quadratic running time, and linear space complexities. Our extensive experiments show that we can reduce the size of large real temporal networks (from multiple domains such as social, co-authorship, and email) significantly without much loss of information. We also show the wide-applicability of NetCondense by leveraging it for several tasks: for example, we use it to understand, explore, and visualize the original datasets and to also speed-up algorithms for the influence-maximization and event detection problems on temporal networks. [ABSTRACT FROM AUTHOR]

The power-law distributions of contact durations and waiting intervals of all pairs of agents together, dubbed as bursts of aggregate pairs, have been found in many realistic opportunistic networks. Many models for such opportunistic networks are under a homogeneous assumption that the distribution from every pair of agents performs the same format as that from all pairs of agents. But our empirical study shows an opposite scenario, e.g., each agent performs Poissonian dynamics while all pairs perform burst dynamics. Therefore, we propose a bottom-up human mobility model to replicate this opportunistic network, and prove that bursts of aggregate pairs can be rooted from individual independent Poissonian self-activity and preferential mobility. Finally we validate our findings with numerical simulations. [ABSTRACT FROM PUBLISHER]

Modern information and communication technologies provide digital traces of human interactive activities, which offer novel avenues to map and analyze temporal features of human interaction networks. This paper explores mesoscopic patterns of human interactive activities from six real-world interaction networks with temporal-topological isomorphic subgraphs, i.e., temporal motifs. We discover two dominant mutual motifs, “Star,” “Ordered-chain,” and one dominant directed motif, “Ping-Pong,” which characterize the interactive patterns of “Leader,” “Queue,” and “Feedback,” respectively. Moreover,temporal dynamics shows that bursts are universal in human mesoscopic patterns, and the evolution of three dominant temporal motifs indicates the existence of characteristic time. Finally, we analyze temporal robustness and generalization to verify that 3-event temporal motifs are a simple yet powerful tool to capture the mesoscopic patterns of human interactive activities. [ABSTRACT FROM AUTHOR]

Many types of social media metadata come in forms of temporal networks, networks where we have information about not only who is in contact with whom but also when contacts happen. In this paper, we review methods to analyze temporal networks developed in the last few years applied to social media data. These methods seek to identify important spreaders and, in more generality, how the temporal and topological structure of interaction affects spreading processes. [ABSTRACT FROM PUBLISHER]

The application of complex network models to communication systems has led to several important results: nonetheless, previous research has often neglected to take into account their temporal properties, which in many real scenarios play a pivotal role. At the same time, network robustness has come extensively under scrutiny. Understanding whether networked systems can undergo structural damage and yet perform efficiently is crucial to both their protection against failures and to the design of new applications. In spite of this, it is still unclear what type of resilience we may expect in a network which continuously changes over time. In this work, we present the first attempt to define the concept of temporal network robustness: we describe a measure of network robustness for time-varying networks and we show how it performs on different classes of random models by means of analytical and numerical evaluation. Finally, we report a case study on a real-world scenario, an opportunistic vehicular system of about 500 taxicabs, highlighting the importance of time in the evaluation of robustness. Particularly, we show how static approximation can wrongly indicate high robustness of fragile networks when adopted in mobile time-varying networks, while a temporal approach captures more accurately the system performance. [ABSTRACT FROM PUBLISHER]

In health care settings, patients who are physically proximate to other patients (co-presence) for a meaningful amount of time may have differential health outcomes depending on who they are in contact with. How to best measure this co-presence, however is an open question and previous approaches have limitations that may make them inappropriate for complex health care settings. Here, we introduce a novel method which we term "consistent co-presence", that implicitly models the many complexities of patient scheduling and movement through a hospital by randomly perturbing the timing of patients' entry time into the health care system. This algorithm generates networks that can be employed in models of patient outcomes, such as 1-year mortality, and are preferred over previously established alternative algorithms from a model comparison perspective. These results indicate that consistent co-presence retains meaningful information about patient-patient interaction, which may affect outcomes relevant to health care practice. Furthermore, the generalizabiity of this approach allows it to be applied to a wide variety of complex systems.