Online multiplayer games are a popular form of social interaction, used by hundreds of millions of individuals. However, little is known about the social networks within these online games, or how they evolve over time. Understanding human social dynamics within massive online games can shed new light on social interactions in general and inform the development of more engaging systems. Here, we study a novel, large friendship network, inferred from nearly 18 billion social interactions over 44 weeks between 17 million individuals in the popular online game Halo:Reach. This network is one of the largest, most detailed temporal interaction networks studied to date, and provides a novel perspective on the dynamics of online friendship networks, as opposed to mere interaction graphs. Initially, this network exhibits strong structural turnover and decays rapidly from a peak size. In the following period, however, both network size and turnover stabilize, producing a dynamic structural equilibrium. In contrast to other studies, we nd that the Halo friendship network is non-densifying: both the mean degree and the average pairwise distance are stable, suggesting that densication cannot occur when maintaining friendships is costly. Finally, players with greater long-term engagement exhibit stronger local clustering, suggesting a group-level social engagement process. These results demonstrate the utility of online games for studying social networks, shed new light on empirical temporal graph patterns, and clarify the claims of universality of network densication.
More recently, researchers have begun to study how time influences @cite_14 and changes network structure @cite_32 . New dynamical patterns, such as densification @cite_9 @cite_29 and shrinking @math -cores @cite_6 , as well as probabilistic models have been identified that shed light on how changes in the underlying processes that produce these networks affect its structure.
@cite_14 @cite_29 @cite_9 @cite_32 @cite_6
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Determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas. Knowledge of such a structure can aid in identifying cause and effect relationships, clustering of similar entities, identification of representative elements and model reduction. The majority of existing results are based on correlation based indices which effectively assume a static relationship between the time series data and are not suitable for detecting interrelatedness when the time series are dynamically related or when the time series involve loops. In this paper, a methodology for identifying the interrelatedness structure of dynamically related time series data is presented that also allows for the presence of loops in the connectivity structure. A linear dynamic graph model is presented where it is assumed that each time series data is the sum of an independent stochastic noise source and a dynamically weighted sum of other time series data. A link is assumed to be present between two time series if the weight of a time series, which is a linear time-invariant filter, is nonzero in the formation of the other. Reconstruction of the link connectivity structure under various scenarios is considered. It is shown that when the linear dynamic graph is allowed to admit non-causal weights, then the links structure can be recovered with the possibility of identifying spurious connections. However, it is shown that the spurious links remain local, where, a spurious link is restricted to be within one hop of a true link. Furthermore, strategies for exact reconstruction of the link structure when the weights are restricted to be causal are developed. The main tools for determining the network topology are based on variations of Wiener filtering. A significant insight provided by the article is that, in the class of network models considered in the paper, the Wiener filter estimating a stochastic process based on other processes remains local in the sense that the Wiener filter utilizes only measurements local to the node being estimated. Networks are present in many fields such as finance, sociology, and transportation. Often these networks are dynamic: they have a structural as well as a temporal aspect. In addition to relations occurring over time, node information is frequently present such as hierarchical structure or time-series data. We present a technique that extends the Massive Sequence View ( msv) for the analysis of temporal and structural aspects of dynamic networks. Using features in the data as well as Gestalt principles in the visualization such as closure, proximity, and similarity, we developed node reordering strategies for the msv to make these features stand out that optionally take the hierarchical node structure into account. This enables users to find temporal properties such as trends, counter trends, periodicity, temporal shifts, and anomalies in the network as well as structural properties such as communities and stars. We introduce the circular msv that further reduces visual clutter. In addition, the (circular) msv is extended to also convey time-series data associated with the nodes. This enables users to analyze complex correlations between edge occurrence and node attribute changes. We show the effectiveness of the reordering methods on both synthetic and a rich real-world dynamic network data set. Time varying problems usually have complex underlying structures represented as dynamic networks where entities and relationships appear and disappear over time. The problem of efficiently performing dynamic link inference is extremely challenging due to the dynamic nature in massive evolving networks especially when there exist sparse connectivities and nonlinear transitional patterns. In this paper, we propose a novel deep learning framework, i.e., Conditional Temporal Restricted Boltzmann Machine (ctRBM), which predicts links based on individual transition variance as well as influence introduced by local neighbors. The proposed model is robust to noise and have the exponential capability to capture nonlinear variance. We tackle the computational challenges by developing an efficient algorithm for learning and inference of the proposed model. To improve the efficiency of the approach, we give a faster approximated implementation based on a proposed Neighbor Influence Clustering algorithm. Extensive experiments on simulated as well as real-world dynamic networks show that the proposed method outperforms existing algorithms in link inference on dynamic networks. The traffic networks reflect the pulse and structure of a city and shows some dynamic characteristic. Previous research in mining structure from networks mostly focus on static networks and fail to exploit the temporal patterns. In this paper, we aim to solve the problem of discovering the urban spatio-temporal structure from time-evolving traffic networks. We model the time-evolving traffic networks into a 3-order tensor, each element of which indicates the volume of traffic from i-th origin area to j-th destination area in k-th time domain. Considering traffic data and urban contextual knowledge together, we propose a regularized Non-negative Tucker Decomposition (rNTD) method, which discovers the spatial clusters, temporal patterns and relations among them simultaneously. Abundant experiments are conducted in a large dataset collected from Beijing. Results show that our method outperforms the baseline method.