The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a " one fits it all " model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.
Among the most well-known evolutionary patterns are the shrinking diameter and densification @cite_33 . A lot of recent work studies link prediction algorithms @cite_26 @cite_19 @cite_29 . Others focus on methods for finding frequent, coherent or dense temporal structures @cite_4 @cite_3 @cite_16 , or the evolution of communities and user behavior @cite_31 @cite_22 .
@cite_26 @cite_4 @cite_33 @cite_22 @cite_29 @cite_3 @cite_19 @cite_31 @cite_16
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Many real-world complex networks, like actor-movie or file-provider relations, have a bipartite nature and evolve over time. Predicting links that will appear in them is one of the main approach to understand their dynamics. Only few works address the bipartite case, though, despite its high practical interest and the specific challenges it raises. We define in this paper the notion of internal links in bipartite graphs and propose a link prediction method based on them. We thoroughly describe the method and its variations, and experimentally compare it to a basic collaborative filtering approach. We present results obtained for a typical practical case. We reach the conclusion that our method performs very well, and we study in details how its parameters may influence obtained results. The problem of finding frequent patterns from graph-based datasets is an important one that finds applications in drug discovery, protein structure analysis, XML querying, and social network analysis among others. In this paper we propose a framework to mine frequent large-scale structures, formally defined as frequent topological structures, from graph datasets. Key elements of our framework include, fast algorithms for discovering frequent topological patterns based on the well known notion of a topological minor, algorithms for specifying and pushing constraints deep into the mining process for discovering constrained topological patterns, and mechanisms for specifying approximate matches when discovering frequent topological patterns in noisy datasets. We demonstrate the viability and scalability of the proposed algorithms on real and synthetic datasets and also discuss the use of the framework to discover meaningful topological structures from protein structure data. How do real graphs evolve over timeq What are normal growth patterns in social, technological, and information networksq Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)). Existing graph generation models do not exhibit these types of behavior even at a qualitative level. We provide a new graph generator, based on a forest fire spreading process that has a simple, intuitive justification, requires very few parameters (like the flammability of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. We also notice that the forest fire model exhibits a sharp transition between sparse graphs and graphs that are densifying. Graphs with decreasing distance between the nodes are generated around this transition point. Last, we analyze the connection between the temporal evolution of the degree distribution and densification of a graph. We find that the two are fundamentally related. We also observe that real networks exhibit this type of relation between densification and the degree distribution. Data confidentiality policies at major social network providers have severely limited researchers' access to large-scale datasets. The biggest impact has been on the study of network dynamics, where researchers have studied citation graphs and content-sharing networks, but few have analyzed detailed dynamics in the massive social networks that dominate the web today. In this paper, we present results of analyzing detailed dynamics in the Renren social network, covering a period of 2 years when the network grew from 1 user to 19 million users and 199 million edges. Rather than validate a single model of network dynamics, we analyze dynamics at different granularities (user-, community- and network- wide) to determine how much, if any, users are influenced by dynamics processes at different scales. We observe in- dependent predictable processes at each level, and find that while the growth of communities has moderate and sustained impact on users, significant events such as network merge events have a strong but short-lived impact that is quickly dominated by the continuous arrival of new users. Targeting interest to match a user with services (e.g. news, products, games, advertisements) and predicting friendship to build connections among users are two fundamental tasks for social network systems. In this paper, we show that the information contained in interest networks (i.e. user-service interactions) and friendship networks (i.e. user-user connections) is highly correlated and mutually helpful. We propose a framework that exploits homophily to establish an integrated network linking a user to interested services and connecting different users with common interests, upon which both friendship and interests could be efficiently propagated. The proposed friendship-interest propagation (FIP) framework devises a factor-based random walk model to explain friendship connections, and simultaneously it uses a coupled latent factor model to uncover interest interactions. We discuss the flexibility of the framework in the choices of loss objectives and regularization penalties and benchmark different variants on the Yahoo! Pulse social networking system. Experiments demonstrate that by coupling friendship with interest, FIP achieves much higher performance on both interest targeting and friendship prediction than systems using only one source of information. How can we describe a large, dynamic graph over time? Is it random? If not, what are the most apparent deviations from randomness -- a dense block of actors that persists over time, or perhaps a star with many satellite nodes that appears with some fixed periodicity? In practice, these deviations indicate patterns -- for example, botnet attackers forming a bipartite core with their victims over the duration of an attack, family members bonding in a clique-like fashion over a difficult period of time, or research collaborations forming and fading away over the years. Which patterns exist in real-world dynamic graphs, and how can we find and rank them in terms of importance? These are exactly the problems we focus on in this work. Our main contributions are (a) formulation: we show how to formalize this problem as minimizing the encoding cost in a data compression paradigm, (b) algorithm: we propose TIMECRUNCH, an effective, scalable and parameter-free method for finding coherent, temporal patterns in dynamic graphs and (c) practicality: we apply our method to several large, diverse real-world datasets with up to 36 million edges and 6.3 million nodes. We show that TIMECRUNCH is able to compress these graphs by summarizing important temporal structures and finds patterns that agree with intuition. Given a snapshot of a social network, can we infer which new interactions among its members are likely to occur in the near future? We formalize this question as the link prediction problem, and develop approaches to link prediction based on measures the "proximity" of nodes in a network. Experiments on large co-authorship networks suggest that information about future interactions can be extracted from network topology alone, and that fairly subtle measures for detecting node proximity can outperform more direct measures. Given publication titles and authors, what can we say about the evolution of scientific topics and communities over time? Which communities shrunk, which emerged, and which split, over time? And, when in time were the turning points? We propose TimeFall, which can automatically answer these questions given a social network graph that evolves over time. The main novelty of the proposed approach is that it needs no user-defined parameters, relying instead on the principle of minimum description length (MDL), to extract the communities, and to find good cut-points in time when communities change abruptly: a cut-point is good, if it leads to shorter data description. We illustrate our algorithm on synthetic and large real datasets, and we show that the results of the TimeFall agree with human intuition. How can we find communities in dynamic networks of socialinteractions, such as who calls whom, who emails whom, or who sells to whom? How can we spot discontinuity time-points in such streams of graphs, in an on-line, any-time fashion? We propose GraphScope, that addresses both problems, using information theoretic principles. Contrary to the majority of earlier methods, it needs no user-defined parameters. Moreover, it is designed to operate on large graphs, in a streaming fashion. We demonstrate the efficiency and effectiveness of our GraphScope on real datasets from several diverse domains. In all cases it produces meaningful time-evolving patterns that agree with human intuition.