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Register a new userModeling temporal networks with bursty activity patterns of nodes and links
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The concept of temporal networks provides a framework to understand how the interaction between system components changes over time. In empirical communication data, we often detect non-Poissonian, so-called bursty behavior in the activity of nodes as well as in the interaction between nodes. However, such reconciliation between node burstiness and link burstiness cannot be explained if the interaction processes on different links are independent of each other. This is because the activity of a node is the superposition of the interaction processes on the links incident to the node and the superposition of independent bursty point processes is not bursty in general. Here we introduce a temporal network model based on bursty node activation and show that it leads to heavy-tailed inter-event time distributions for both node dynamics and link dynamics. Our analysis indicates that activation processes intrinsic to nodes give rise to dynamical correlations across links. Our framework offers a way to model competition and correlation between links, which is key to understanding dynamical processes in various systems.
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The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule.
Identifying important nodes is one of the central tasks in network science, which is crucial for analyzing the structure of a network and understanding the dynamical processes on a network. Most real-world systems are time-varying and can be well represented as temporal networks. Motivated by the classic gravity model in physics, we propose a temporal gravity model to identify influential nodes in temporal networks. Two critical elements in the gravity model are the masses of the objects and the distance between two objects. In the temporal gravity model, we treat nodes as the objects, basic node properties, such as static and temporal properties, as the nodes masses. We define temporal distances, i.e., fastest arrival distance and temporal shortest distance, as the distance between two nodes in our model. We utilize our model as well as the baseline centrality methods on important nodes identification. Experimental results on ten real-world datasets show that the temporal gravity model outperforms the baseline methods in quantifying node structural influence. Moreover, when we use the temporal shortest distance as the distance between two nodes, our model is robust and performs the best in quantifying node spreading influence compared to the baseline methods.
In this Letter, we empirically study the influence of reciprocal links, in order to understand its role in affecting the structure and function of directed social networks. Experimental results on two representative datesets, Sina Weibo and Douban, demonstrate that the reciprocal links indeed play a more important role than non-reciprocal ones in both spreading information and maintaining the network robustness. In particular, the information spreading process can be significantly enhanced by considering the reciprocal effect. In addition, reciprocal links are largely responsible for the connectivity and efficiency of directed networks. This work may shed some light on the in-depth understanding and application of the reciprocal effect in directed online social networks.
Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-removed (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach we derive, in the long time limit, analytical predictions for the epidemic threshold as a function of the parameters describing the distribution of activities and the strength of the memory effects. Our results show that memory reduces the threshold, which is the same for SIS and SIR dynamics, therefore favouring epidemic spreading. The theoretical approach perfectly agrees with numerical simulations in the long time asymptotic regime. Strong aging effects are present in the preasymptotic regime and the epidemic threshold is deeply affected by the starting time of the epidemics. We discuss in detail the origin of the model-dependent preasymptotic corrections, whose understanding could potentially allow for epidemic control on correlated temporal networks.
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model proposed by Barabasi and Albert: nodes are added to the network connecting preferably to other nodes that are more connected. We also presented models that consider more representative elements from social perspectives, such as the homophily between the vertices or the fitness that each node has to build connections. Furthermore, we showed a version of these models including the Euclidean distance between the nodes as a preferential attachment rule. Our objective is to investigate the basic properties of these networks as distribution of connectivity, degree correlation, shortest path, cluster coefficient and how these characteristics are affected by the preferential attachment rules. Finally, we also provided a comparison of these synthetic networks with real ones. We found that characteristics as homophily, fitness and geographic distance are significant preferential attachment rules to modeling real networks. These rules can change the degree distribution form of these synthetic network models and make them more suitable to model real networks.
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