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.
Time-aware ranking Closely related to dynamic network analysis is the problem of time-aware ranking of Web pages in information retrieval. This research is motivated by the observation @cite_22 that PageRank's Web ranking algorithm is biased against newer pages, which may not have had enough time to accumulate links to give it a high rank. Several methods have been proposed to address the recency bias in PageRank, including @cite_22 @cite_15 @cite_29 @cite_14 . In general terms, these methods weigh edges in the network by age, with newer edges contributing more heavily to a page's importance. Our motivation is different. Rather than focus on improving the rank of newer nodes, we focus instead on defining a time-aware centrality metric that takes the temporal order of edges into account.
@cite_14 @cite_15 @cite_29 @cite_22
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Many real applications in real-time news stream advertising call for efficient processing of long queries against short text. In such applications, dynamic news feeds are regarded as queries to match against an advertisement (ad) database for retrieving the k most relevant ads. The existing approaches to keyword retrieval cannot work well in this search scenario when queries are triggered at a very high frequency. To address the problem, we introduce new techniques to significantly improve search performance. First, we devise a two-level partitioning for tight upper bound estimation and a lazy evaluation scheme to delay full evaluation of unpromising candidates, which can bring three to four times performance boosting in a database with 7 million ads. Second, we propose a novel rank-aware block-oriented inverted index to further improve performance. In this index scheme, each entry in an inverted list is assigned a rank according to its importance in the ad. Then, we introduce a block-at-a-time search strategy based on the index scheme to support a much tighter upper bound estimation and a very early termination. We have conducted experiments with real datasets, and the results show that the rank-aware method can further improve performance by an order of magnitude. Popular reputation systems for linked networks can be manipulated by spammers who strategically place links. The reputation of node v is interpreted as the world's opinion of v's importance. In PageRank [4], v's own opinion can be seen to have considerable influence on her reputation, where v expresses a high opinion of herself by participating in short directed cycles. In contrast, we show that expected hitting time -- the time to reach v in a random walk -- measures essentially the same quantity as PageRank, but excludes v's opinion. We make these notions precise, and show that a reputation system based on hitting time resists tampering by individuals or groups who strategically place outlinks. We also present an algorithm to efficiently compute hitting time for all nodes in a massive graph; conventional algorithms do not scale adequately. 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 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].