Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to static networks. Most networks, on the other hand, are dynamic in nature, evolving over time through the addition or deletion of nodes and edges. A popular approach to analyzing such networks represents them by a static network that aggregates all edges observed over some time period. This approach, however, under or overestimates centrality of some nodes. We address this problem by introducing a novel centrality metric for dynamic network analysis. This metric exploits an intuition that in order for one node in a dynamic network to influence another over some period of time, there must exist a path that connects the source and destination nodes through intermediaries at different times. We demonstrate on an example network that the proposed metric leads to a very different ranking than analysis of an equivalent static network. We use dynamic centrality to study a dynamic citations network and contrast results to those reached by static network analysis.
Authors of @cite_18 considered the temporal order of edges in the flow of information on a network. They proposed EventRank algorithm, a modification of PageRank, that takes into account a temporal sequence of events, e.g., spread of an email message, in order to calculate importance of nodes in a network. This approach takes into account the effect of the on ranking. In contrast, we consider the effect of the on ranking. These approaches are somewhat related: our method can be said to estimate the expected value of all temporal sequences taking place on the network.
@cite_18
1967947187 2051381393 2010682628 1752265245
Node-ranking algorithms for (social) networks do not respect the sequence of events from which the network is constructed, but rather measure rank on the aggregation of all data. For data sets that relate to the flow of information (e.g., email), this loss of information can obscure the true relative importances of individuals in the network. We present EventRank, a framework for ranking algorithms that respect event sequences and provide a natural way of tracking changes in ranking over time. We compare the performance of a number of ranking algorithms using a large organizational data set consisting of approximately 1 million emails involving over 600 users, including an evaluation of how the email-based ranking correlates with known organizational hierarchy. In this paper, we analyze the efficiency of Monte Carlo methods for incremental computation of PageRank, personalized PageRank, and similar random walk based methods (with focus on SALSA), on large-scale dynamically evolving social networks. We assume that the graph of friendships is stored in distributed shared memory, as is the case for large social networks such as Twitter. For global PageRank, we assume that the social network has n nodes, and m adversarially chosen edges arrive in a random order. We show that with a reset probability of e, the expected total work needed to maintain an accurate estimate (using the Monte Carlo method) of the PageRank of every node at all times is [EQUATION]. This is significantly better than all known bounds for incremental PageRank. For instance, if we naively recompute the PageRanks as each edge arrives, the simple power iteration method needs [EQUATION] total time and the Monte Carlo method needs O(mn e) total time; both are prohibitively expensive. We also show that we can handle deletions equally efficiently. We then study the computation of the top k personalized PageRanks starting from a seed node, assuming that personalized PageRanks follow a power-law with exponent α q ln n random walks starting from every node for large enough constant q (using the approach outlined for global PageRank), then the expected number of calls made to the distributed social network database is O(k (R(1-α) α)). We also present experimental results from the social networking site, Twitter, verifying our assumptions and analyses. The overall result is that this algorithm is fast enough for real-time queries over a dynamic social network. In this paper we study gossip based information spreading with bounded message sizes. We use algebraic gossip to disseminate k distinct messages to all n nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of O((k + log n + D)Δ) rounds with high probability, where D and Δ are the diameter and the maximum degree in the network, respectively. For many topologies and selections of k this bound improves previous results, in particular, for graphs with a constant maximum degree it implies that uniform gossip is order optimal and the stopping time is Θ(k + D). To eliminate the factor of Δ from the upper bound we propose a non-uniform gossip protocol, TAG, which is based on algebraic gossip and an arbitrary spanning tree protocol S. The stopping time of TAG is O(k+ log n + d(S) + t(S)), where t(S) is the stopping time of the spanning tree protocol, and d(S) is the diameter of the spanning tree. We provide two general cases in which this bound leads to an order optimal protocol. The first is for k=Ω(n), where, using a simple gossip broadcast protocol that creates a spanning tree in at most linear time, we show that TAG finishes after Θ(n) rounds for any graph. The second uses a sophisticated, recent gossip protocol to build a fast spanning tree on graphs with large weak conductance. In turn, this leads to the optimally of TAG on these graphs for k=Ω(polylog(n)). The technique used in our proofs relies on queuing theory, which is an interesting approach that can be useful in future gossip analysis. In a network, identifying all vertices whose PageRank is more than a given threshold value Δ is a basic problem that has arisen in Web and social network analyses. In this paper, we develop a nearly optimal, sublinear time, randomized algorithm for a close variant of this problem. When given a directed network G=(V,E), a threshold value Δ, and a positive constant c>3, with probability 1−o(1), our algorithm will return a subset S⊆V with the property that S contains all vertices of PageRank at least Δ and no vertex with PageRank less than Δ c. The running time of our algorithm is always @math . In addition, our algorithm can be efficiently implemented in various network access models including the Jump and Crawl query model recently studied by [6], making it suitable for dealing with large social and information networks. As part of our analysis, we show that any algorithm for solving this problem must have expected time complexity of @math . Thus, our algorithm is optimal up to logarithmic factors. Our algorithm (for identifying vertices with significant PageRank) applies a multi-scale sampling scheme that uses a fast personalized PageRank estimator as its main subroutine. For that, we develop a new local randomized algorithm for approximating personalized PageRank which is more robust than the earlier ones developed by Jeh and Widom [9] and by Andersen, Chung, and Lang [2].