Null models for dynamic centrality in temporal networks

Identifying influential spreaders is an important issue for capturing the dynamics of information diffusion in temporal networks. Most of the identification of influential spreaders in previous researches were focused on analysing static networks, rarely highlighted on dynamics. However, those measures which are proposed for static topologies only, unable to faithfully capture the effect of temporal variations on the importance of nodes. In this paper, a shortest temporal path algorithm is proposed for calculating the minimum time that information interaction between nodes. This algorithm can effectively find out the shortest temporal path when considering the network integrity. On the basis of this, the temporal efficiency centrality (TEC) algorithm in temporal networks is proposed, which identify influential nodes by removing each node and taking the variation of the whole network into consideration at the same time. To evaluate the effectiveness of this algorithm, we conduct the experiment on four real-world temporal networks for Susceptible-Infected-Recovered (SIR) model. By employing the imprecision and the Kendall’s au coefficient, The results show that this algorithm can effectively evaluate the importance of nodes in temporal networks.

Identifying important nodes in complex networks is a fundamental problem in network analysis. Although a plethora of measures has been proposed to identify important nodes in static (i.e., time-invariant) networks, there is a lack of tools in the context of temporal networks (i.e., networks whose connectivity dynamically changes over time). The aim of this paper is to propose a system-theoretic approach for identifying important nodes in temporal networks. In this direction, we first propose a generalization of the popular Katz centrality measure to the family of Markovian temporal networks using tools from the theory of Markov jump linear systems. We then show that Katz centrality in Markovian temporal networks can be efficiently computed using linear programming. Finally, we propose a convex program for optimizing the Katz centrality of a given node by tuning the weights of the temporal network in a cost-efficient manner. Numerical simulations illustrate the effectiveness of the obtained results.

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.

The research on node importance identification for temporal networks has attracted much attention. In this work, combined with the multi-layer coupled network analysis method, an optimized supra-adjacency matrix (OSAM) modeling method was proposed. In the process of constructing an optimized super adjacency matrix, the intra-layer relationship matrixes were improved by introducing the edge weight. The inter-layer relationship matrixes were formed by improved similarly and the inter-layer relationship is directional by using the characteristics of directed graphs. The model established by the OSAM method accurately expresses the structure of the temporal network and considers the influence of intra- and inter-layer relationships on the importance of nodes. In addition, an index was calculated by the average of the sum of the eigenvector centrality indices for a node in each layer and the node importance sorted list was obtained from this index to express the global importance of nodes in temporal networks. The experimental results on three real temporal network datasets Enron, Emaildept3, and Workspace showed that compared with the SAM and the SSAM methods, the OSAM method has a faster message propagation rate and larger message coverage and better SIR and NDCG@10 indicators.

This chapter presents the existing modelling frameworks for multiplex and multilayer networks. Multiplex network models are divided into growing multiplex network models and null models of multiplex networks. Growing multiplex networks are here shown to explain the main dynamical rules responsible to the emergent properties of multiplex networks, including the scale-free degree distribution, interlayer degree correlations and multilayer communities. Null models of multiplex networks are described in the context of maximum-entropy multiplex network ensembles. Randomization algorithms to test the relevant of network properties against null models are here described. Moreover, Multi-slice temporal networks Models capturing main properties of real temporal network data are presented. Finally, null models of general multilayer networks and networks of networks are characterized.

In order to meet passengers’ demands for increasing travel efficiency, the structure of China’s airport network will become more and more complex, and its operating environment has become more complex, so, it is important to measure the robustness of China’s airport network under the influence of complex disturbance factors. This paper proposes an airport network robustness analysis method based on the multi-layer temporal complex network model (MTNM) by introducing the time attribute. Firstly, we establish the network structure characteristics such as temporal degree, temporal closeness centrality (TC), and temporal betweenness centrality (TB) of airport network nodes, and take temporal network efficiency and temporal maximum connected subgraph as indicators; then inflection points of loss fitting curves for temporal network characteristics metrics under random attacks and deliberate attacks can be identified to evaluate network robustness. The results show that compared with static network, using multi-layer temporal network model can describe the performance characteristics of the network more accurately.

Aiming at enhancing geographical road network analysis from a network science perspective, we introduce a novel problem of analyzing the road network in a city, and consider providing a new network centrality metric that could be useful for that problem. The problem addresses vehicular evacuation in urban settings. During emergency and disaster scenarios of vehicular evacuation, the shortest distance routes might not always be the most optimal. Instead, routes that are easier to traverse can be more crucial, even if they involve detours. Also, destinations for evacuation do not necessarily have to be restricted to traditional facilities; broad and well-maintained streets might also serve as suitable alternatives. We focus on the streets as the basic units of the road network to be investigated, and consider a scenario in which people efficiently move from starting intersections around their current places to designated goal streets, following the routes of easiest traversal. For the road network, we employ its topological representation, where vertices and edges correspond to streets and intersections between them, respectively. We thus represent the road network as a vertex-weighted graph, where the weight of each vertex reflects its ease of traversal. By appropriately extending the recently developed edge-centrality metric, “salience”, to this vertex-weighted graph, we construct a new network centrality metric to detect critical streets for the newly introduced problem. Using a toy model of road network and real-world urban road networks obtained from OpenStreetMap, we experimentally reveal its distinctive characteristics by comparing it with several baselines. Moreover, we demonstrate that the proposed network centrality metric can successfully find critical streets for vehicular evacuation, which are difficult to detect using baseline methods.

Knowledge of species composition and their interactions, in the form of interaction networks, is required to understand processes shaping their distribution over time and space. As such, comparing ecological networks along environmental gradients represents a promising new research avenue to understand the organization of life. Variation in the position and intensity of links within networks along environmental gradients may be driven by turnover in species composition, by variation in species abundances and by abiotic influences on species interactions. While investigating changes in species composition has a long tradition, so far only a limited number of studies have examined changes in species interactions between networks, often with differing approaches. Here, we review studies investigating variation in network structures along environmental gradients, highlighting how methodological decisions about standardization can influence their conclusions. Due to their complexity, variation among ecological networks is frequently studied using properties that summarize the distribution or topology of interactions such as number of links, connectance, or modularity. These properties can either be compared directly or using a procedure of standardization. While measures of network structure can be directly related to changes along environmental gradients, standardization is frequently used to facilitate interpretation of variation in network properties by controlling for some co-variables, or via null models. Null models allow comparing the deviation of empirical networks from random expectations and are expected to provide a more mechanistic understanding of the factors shaping ecological networks when they are coupled with functional traits. As an illustration, we compare approaches to quantify the role of trait matching in driving the structure of plant-hummingbird mutualistic networks, i.e. a direct comparison, standardized by null models and hypothesis-based metaweb. Overall, our analysis warns against a comparison of studies that rely on distinct forms of standardization, as they are likely to highlight different signals. Fostering a better understanding of the analytical tools available and the signal they detect will help produce deeper insights into how and why ecological networks vary along environmental gradients.

In network analysis, the betweenness centrality of a node informally captures\nthe fraction of shortest paths visiting that node. The computation of the\nbetweenness centrality measure is a fundamental task in the analysis of modern\nnetworks, enabling the identification of the most central nodes in such\nnetworks. Additionally to being massive, modern networks also contain\ninformation about the time at which their events occur. Such networks are often\ncalled temporal networks. The temporal information makes the study of the\nbetweenness centrality in temporal networks (i.e., temporal betweenness\ncentrality) much more challenging than in static networks (i.e., networks\nwithout temporal information). Moreover, the exact computation of the temporal\nbetweenness centrality is often impractical on even moderately-sized networks,\ngiven its extremely high computational cost. A natural approach to reduce such\ncomputational cost is to obtain high-quality estimates of the exact values of\nthe temporal betweenness centrality. In this work we present ONBRA, the first\nsampling-based approximation algorithm for estimating the temporal betweenness\ncentrality values of the nodes in a temporal network, providing rigorous\nprobabilistic guarantees on the quality of its output. ONBRA is able to compute\nthe estimates of the temporal betweenness centrality values under two different\noptimality criteria for the shortest paths of the temporal network. In\naddition, ONBRA outputs high-quality estimates with sharp theoretical\nguarantees leveraging on the \\emph{empirical Bernstein bound}, an advanced\nconcentration inequality. Finally, our experimental evaluation shows that ONBRA\nsignificantly reduces the computational resources required by the exact\ncomputation of the temporal betweenness centrality on several real world\nnetworks, while reporting high-quality estimates with rigorous guarantees.\n

BackgroundMost existing algorithms for modeling and analyzing molecular networks assume a static or time-invariant network topology. Such view, however, does not render the temporal evolution of the underlying biological process as molecular networks are typically “re-wired” over time in response to cellular development and environmental changes. In our previous work, we formulated the inference of time-varying or dynamic networks as a tracking problem, where the target state is the ensemble of edges in the network. We used the Kalman filter to track the network topology over time. Unfortunately, the output of the Kalman filter does not reflect known properties of molecular networks, such as sparsity.ResultsTo address the problem of inferring sparse time-varying networks from a set of under-sampled measurements, we propose the Approximate Kernel RecONstruction (AKRON) Kalman filter. AKRON supersedes the Lasso regularization by starting from the Lasso-Kalman inferred network and judiciously searching the space for a sparser solution. We derive theoretical bounds for the optimality of AKRON. We evaluate our approach against the Lasso-Kalman filter on synthetic data. The results show that not only does AKRON-Kalman provide better reconstruction errors, but it is also better at identifying if edges exist within a network. Furthermore, we perform a real-world benchmark on the lifecycle (embryonic, larval, pupal, and adult stages) of the Drosophila Melanogaster.ConclusionsWe show that the networks inferred by the AKRON-Kalman filter are sparse and can detect more known gene-to-gene interactions for the Drosophila melanogaster than the Lasso-Kalman filter. Finally, all of the code reported in this contribution will be publicly available.

This work explores the application of complex network centrality metrics as a means to predict the relative location performance of a task manager within a network topology. Our studies examine the problem of optimizing the location of a tasking and data collection node in a master-slave distributed tasking model. Through a series of analytical and emulation experiment-based measurements we examine the correlation between the workflow completion delay and a series of candidate network centrality metrics. Our hypothesis is that centrality based metrics can serve as an engineering guide in planning or managing complex distributed network service deployments. Our initial analytical network experiments are represented by a series of different styles of randomly generated topologies as well as a series of network snapshots from a modeled heterogeneous network topology. Using the baseline analytical model we demonstrate correlation statistics between certain node centrality metrics and the total tasking delay experienced when the task manager is placed at a candidate location. Next, we obtain a set of performance results through emulation experimentation using working distributed coordination software, ad hoc routing, bandwidth restrictions, and network delay within an emulated mesh topology. We perform a series of experiments with varying network diameters and we conclude by reviewing the correlation trends between delay performance prediction and several centrality metrics. We also present a discussion of additional open issues and future work planned.

Here, we deal with a model of multitype network with nonpreferential attachment growth. The connection between two nodes depends asymmetrically on their types, reflecting the implication of time order in temporal networks. Based upon graph limit theory, we analytically determined the limit of the network model characterized by a kernel, in the sense that the number of copies of any fixed subgraph converges when network size tends to infinity. The results are confirmed by extensive simulations. Our work thus provides a theoretical framework for quantitatively understanding grown temporal complex networks as a whole.

An important feature of all real-world networks is that the network structure changes over time. Due to this dynamic nature, it becomes difficult to propose suitable growth models that can explain the various important characteristic properties of these networks. In fact, in many application oriented studies only knowing these properties is sufficient. We, in this paper show that even if the network structure at a future time point is not available one can still manage to estimate its properties. We propose a novel method to map a temporal network to a set of time series instances, analyze them and using a standard forecast model of time series, try to predict the properties of a temporal network at a later time instance. We mainly focus on the temporal network of human face- to-face contacts and observe that it represents a stochastic process with memory that can be modeled as ARIMA. We use cross validation techniques to find the percentage accuracy of our predictions. An important observation is that the frequency domain properties of the time series obtained from spectrogram analysis could be used to refine the prediction framework by identifying beforehand the cases where the error in prediction is likely to be high. This leads to an improvement of 7.96% (for error level <= 20%) in prediction accuracy on an average across all datasets. As an application we show how such prediction scheme can be used to launch targeted attacks on temporal networks.

This article proposes urban network models as instruments to measure urban form, structure, and function indicators for the assessment of the sustainable mobility of urban areas, thanks to their capacity to describe the detail of a local environment in the context of a wider city‐region. Drawing from the features of existing street network models that offer disaggregate, scalable, and relational analysis of the spatial configuration of urban areas, it presents a multimodal urban network (MMUN) model that describes an urban environment using three systems—private transport (i.e., car, bicycle, and pedestrian), public transport (i.e., rail, tram, metro, and bus), and land use. This model offers a unifying framework that allows the use of a range of analysis metrics and conceptions of distance (i.e., physical, topological, and cognitive), and aims to be simple and applicable in practice. An implementation of theMMUNis created for the Randstad city‐region in theNetherlands. This is analyzed with network centrality measures in a series of experiments, testing its performance against empirical data. The experiments yield conclusions regarding the use of different distance parameters, the choice of network centrality metrics, and the relevant combinations of multimodal layers to describe the structure and configuration of a city‐region.

Temporal networks are graphs in which edges have temporal labels, specifying their starting times and their traversal times. Several notions of distances between two nodes in a temporal network can be analyzed, by referring, for example, to the earliest arrival time or to the latest starting time of a temporal path connecting the two nodes. In this paper, we mostly refer to the notion of temporal reachability by using the earliest arrival time. In particular, we first show how the sketch approach, which has already been used in the case of classical graphs, can be applied to the case of temporal networks in order to approximately compute the sizes of the temporal cones of a temporal network. By making use of this approach, we subsequently show how we can approximate the temporal neighborhood function (that is, the number of pairs of nodes reachable from one another in a given time interval) of large temporal networks in a few seconds. Finally, we apply our algorithm in order to analyze and compare the behavior of 25 public transportation temporal networks. Our results can be easily adapted to the case in which we want to refer to the notion of distance based on the latest starting time.