Degree distribution models are incredibly important tools for analyzing and understanding the structure and formation of social networks, and can help guide the design of efficient graph algorithms. In particular, the Power-law degree distribution has long been used to model the structure of online social networks, and is the basis for algorithms and heuristics in graph applications such as influence maximization and social search. Along with recent measurement results, our interest in this topic was sparked by our own experimental results on social graphs that deviated significantly from those predicted by a Power-law model. In this work, we seek a deeper understanding of these deviations, and propose an alternative model with significant implications on graph algorithms and applications. We start by quantifying this artifact using a variety of real social graphs, and show that their structures cannot be accurately modeled using elementary distributions including the Power-law. Instead, we propose the Pareto-Lognormal (PLN) model, verify its goodness-of-fit using graphical and statistical methods, and present an analytical study of its asymptotical differences with the Power-law. To demonstrate the quantitative benefits of the PLN model, we compare the results of three wide-ranging graph applications on real social graphs against those on synthetic graphs generated using the PLN and Power-law models. We show that synthetic graphs generated using PLN are much better predictors of degree distributions in real graphs, and produce experimental results with errors that are orders-of-magnitude smaller than those produced by the Power-law model.
Social Applications and Systems. We have shown that our proposed PLN is statistically more accurate in describing OSNs than the seminal Power-law model. We believe that many social applications and protocols designed based on the Power-law assumption need to be re-evaluated, especially algorithms and protocols that rely on the population of high degree nodes or their connectivity. Examples include distributed resource replication strategies to minimize routing delay and social search, epidemics dissemination strategies to maximize information spread @cite_25 , landmark selection strategies to accurately predicts shortest paths in graphs @cite_42 , community detection to improve social recommendation systems, and social attack strategies @cite_5 .
@cite_5 @cite_42 @cite_25
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State-of-the-art techniques for probability sampling of users of online social networks (OSNs) are based on random walks on a single social relation (typically friendship). While powerful, these methods rely on the social graph being fully connected. Furthermore, the mixing time of the sampling process strongly depends on the characteristics of this graph. In this paper, we observe that there often exist other relations between OSN users, such as membership in the same group or participation in the same event. We propose to exploit the graphs these relations induce, by performing a random walk on their union multigraph. We design a computationally efficient way to perform multigraph sampling by randomly selecting the graph on which to walk at each iteration. We demonstrate the benefits of our approach through (i) simulation in synthetic graphs, and (ii) measurements of Last.fm- an Internet website for music with social networking features. More specifically, we show that multigraph sampling can obtain a representative sample and faster convergence, even when the individual graphs fail, i.e., are disconnected or highly clustered. Online social networks (OSNs) like Facebook, and Myspace recommend new friends to registered users based on local features of the graph (i.e. based on the number of common friends that two users share). However, OSNs do not exploit the whole structure of the network. Instead, they consider only pathways of maximum length 2 between a user and his candidate friends. On the other hand, there are global approaches, which detect the overall path structure in a network, being computationally prohibitive for huge-size social networks. In this paper, we define a basic node similarity measure that captures effectively local graph features. We also exploit global graph features introducing transitive node similarity. Moreover, we derive variants of our method that apply in signed networks. We perform extensive experimental comparison of the proposed method against existing recommendation algorithms using synthetic and real data sets (Facebook, Hi5 and Epinions). Our experimental results show that our FriendTNS algorithm outperforms other approaches in terms of accuracy and it is also time efficient. We show that a significant accuracy improvement can be gained by using information about both positive and negative edges. Online social networks (OSNs) have become one of the most effective channels for marketing and advertising. Since users are often influenced by their friends, “word-of-mouth” exchanges, so-called viral marketing, in social networks can be used to increase product adoption or widely spread content over the network. The common perception of viral marketing about being cheap, easy, and massively effective makes it an ideal replacement of traditional advertising. However, recent studies have revealed that the propagation often fades quickly within only few hops from the sources, counteracting the assumption on the self-perpetuating of influence considered in literature. With only limited influence propagation, is massively reaching customers via viral marketing still affordable? How do we economically spend more resources to increase the spreading speed? We investigate the cost-effective massive viral marketing problem, taking into the consideration the limited influence propagation. Both analytical analysis based on power-law network theory and numerical analysis demonstrate that the viral marketing might involve costly seeding. To minimize the seeding cost, we provide mathematical programming to find optimal seeding for medium-size networks and propose VirAds, an efficient algorithm, to tackle the problem on large-scale networks. VirAds guarantees a relative error bound of @math from the optimal solutions in power-law networks and outperforms the greedy heuristics that realizes on the degree centrality. Moreover, we also show that, in general, approximating the optimal seeding within a ratio better than @math is unlikely possible. Online social networks (OSNs) have become popular destinations for connecting friends and sharing information. Recent statistics suggest that OSN users regularly share contents from video sites, and a significant amount of requests of the video sites are indeed from them nowadays. These behaviors have substantially changed the workload of online video services. To better understand this paradigm shift, we conduct a long-term and extensive measurement of video sharing in RenRen, the largest Facebook-like OSN in China. In this paper, we focus on the video popularity distribution and evolution. In particular, we find that the video popularity distribution exhibits perfect power-law feature (while videos in YouTube exhibit a power-law waist with a long truncated tail). Moreover, we observe that the requests for the new published videos generally experience two or three days latency to reach the peak value, and then change dynamically with a series of unpredictable bursts (while in YouTube, videos reach the global peak immediately after introduction to the system, and then the accesses generally decrease overtime, except possibly on some special days). These differences can raise new challenges to content providers. For example, the video popularity is now hard to predict based on their historical requests. We further develop a simple yet effective model to simulate user requests process across videos in OSNs. Trace-based simulation shows that it can well capture the observed features.