Observations on the Dynamic Evolution of Peer-to-Peer Networks

A fundamental theoretical challenge in peer-to-peer systems is proving statements about the evolution of the system while nodes are continuously joining and leaving. Because the system will operate for an infinite time, performance measures based on runtime are uninformative; instead, we must study the rate at which nodes consume resources to maintain the system state

Do Diffusion Protocols Govern Cascade Growth?

Large cascades can develop in online social networks as people share information with one another. Though simple reshare cascades have been studied extensively, the full range of cascading behaviors on social media is much more diverse. Here we study how diffusion protocols, or the social exchanges that enable information transmission, affect cascade growth, analogous to the way communication protocols define how information is transmitted from one point to another. Studying 98 of the largest information cascades on Facebook, we find a wide range of diffusion protocols - from cascading reshares of images, which use a simple protocol of tapping a single button for propagation, to the ALS Ice Bucket Challenge, whose diffusion protocol involved individuals creating and posting a video, and then nominating specific others to do the same. We find recurring classes of diffusion protocols, and identify two key counterbalancing factors in the construction of these protocols, with implications for a cascade's growth: the effort required to participate in the cascade, and the social cost of staying on the sidelines. Protocols requiring greater individual effort slow down a cascade's propagation, while those imposing a greater social cost of not participating increase the cascade's adoption likelihood. The predictability of transmission also varies with protocol. But regardless of mechanism, the cascades in our analysis all have a similar reproduction number ($\approx$ 1.8), meaning that lower rates of exposure can be offset with higher per-exposure rates of adoption. Last, we show how a cascade's structure can not only differentiate these protocols, but also be modeled through branching processes. Together, these findings provide a framework for understanding how a wide variety of information cascades can achieve substantial adoption across a network.Comment: ICWSM 201

Fast matrix computations for pair-wise and column-wise commute times and Katz scores

We first explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments, and quadrature developed in the numerical linear algebra community. They rely on the Lanczos process and provide upper and lower bounds on an estimate of the pair-wise scores. We also explore methods to approximate the commute times and Katz scores from a node to all other nodes in the graph. Here, our approach for the commute times is based on a variation of the conjugate gradient algorithm, and it provides an estimate of all the diagonals of the inverse of a matrix. Our technique for the Katz scores is based on exploiting an empirical localization property of the Katz matrix. We adopt algorithms used for personalized PageRank computing to these Katz scores and theoretically show that this approach is convergent. We evaluate these methods on 17 real world graphs ranging in size from 1000 to 1,000,000 nodes. Our results show that our pair-wise commute time method and column-wise Katz algorithm both have attractive theoretical properties and empirical performance.Comment: 35 pages, journal version of http://dx.doi.org/10.1007/978-3-642-18009-5_13 which has been submitted for publication. Please see http://www.cs.purdue.edu/homes/dgleich/publications/2011/codes/fast-katz/ for supplemental code

Navigability is a Robust Property

The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random destination selected from a carefully crafted probability distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it allows greedy routing to successfully deliver messages between any two vertices in a polylogarithmic number of steps. We prove that navigability is an inherent property of many random networks, arising without coordination, or even independence assumptions

An algorithmic approach to social networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 109-120).Social networks consist of a set of individuals and some form of social relationship that ties the individuals together. In this thesis, we use algorithmic techniques to study three aspects of social networks: (1) we analyze the "small-world" phenomenon by examining the geographic patterns of friendships in a large-scale social network, showing how this linkage pattern can itself explain the small-world results; (2) using existing patterns of friendship in a social network and a variety of graph-theoretic techniques, we show how to predict new relationships that will form in the network in the near future; and (3) we show how to infer social connections over which information flows in a network, by examining the times at which individuals in the network exhibit certain pieces of information, or interest in certain topics. Our approach is simultaneously theoretical and data-driven, and our results are based upon real experiments on real social-network data in addition to theoretical investigations of mathematical models of social networks.by David Liben-Nowell.Ph.D

The evolution of interdisciplinarity in physics research

Science, being a social enterprise, is subject to fragmentation into groups that focus on specialized areas or topics. Often new advances occur through cross-fertilization of ideas between sub-fields that otherwise have little overlap as they study dissimilar phenomena using different techniques. Thus to explore the nature and dynamics of scientific progress one needs to consider the large-scale organization and interactions between different subject areas. Here, we study the relationships between the sub-fields of Physics using the Physics and Astronomy Classification Scheme (PACS) codes employed for self-categorization of articles published over the past 25 years (1985-2009). We observe a clear trend towards increasing interactions between the different sub-fields. The network of sub-fields also exhibits core-periphery organization, the nucleus being dominated by Condensed Matter and General Physics. However, over time Interdisciplinary Physics is steadily increasing its share in the network core, reflecting a shift in the overall trend of Physics research.Comment: Published version, 10 pages, 8 figures + Supplementary Informatio

Summarizing Diverging String Sequences, with Applications to Chain-Letter Petitions

Algorithms to find optimal alignments among strings, or to find a parsimonious summary of a collection of strings, are well studied in a variety of contexts, addressing a wide range of interesting applications. In this paper, we consider chain letters, which contain a growing sequence of signatories added as the letter propagates. The unusual constellation of features exhibited by chain letters (one-ended growth, divergence, and mutation) make their propagation, and thus the corresponding reconstruction problem, both distinctive and rich. Here, inspired by these chain letters, we formally define the problem of computing an optimal summary of a set of diverging string sequences. From a collection of these sequences of names, with each sequence noisily corresponding to a branch of the unknown tree $T$ representing the letter's true dissemination, can we efficiently and accurately reconstruct a tree $T' \approx T$? In this paper, we give efficient exact algorithms for this summarization problem when the number of sequences is small; for larger sets of sequences, we prove hardness and provide an efficient heuristic algorithm. We evaluate this heuristic on synthetic data sets chosen to emulate real chain letters, showing that our algorithm is competitive with or better than previous approaches, and that it also comes close to finding the true trees in these synthetic datasets.Comment: 18 pages, 6 figures. Accepted to Combinatorial Pattern Matching (CPM) 202

From Relational Data to Graphs: Inferring Significant Links using Generalized Hypergeometric Ensembles

The inference of network topologies from relational data is an important problem in data analysis. Exemplary applications include the reconstruction of social ties from data on human interactions, the inference of gene co-expression networks from DNA microarray data, or the learning of semantic relationships based on co-occurrences of words in documents. Solving these problems requires techniques to infer significant links in noisy relational data. In this short paper, we propose a new statistical modeling framework to address this challenge. It builds on generalized hypergeometric ensembles, a class of generative stochastic models that give rise to analytically tractable probability spaces of directed, multi-edge graphs. We show how this framework can be used to assess the significance of links in noisy relational data. We illustrate our method in two data sets capturing spatio-temporal proximity relations between actors in a social system. The results show that our analytical framework provides a new approach to infer significant links from relational data, with interesting perspectives for the mining of data on social systems.Comment: 10 pages, 8 figures, accepted at SocInfo201

Collaborative filtering with diffusion-based similarity on tripartite graphs

Collaborative tags are playing more and more important role for the organization of information systems. In this paper, we study a personalized recommendation model making use of the ternary relations among users, objects and tags. We propose a measure of user similarity based on his preference and tagging information. Two kinds of similarities between users are calculated by using a diffusion-based process, which are then integrated for recommendation. We test the proposed method in a standard collaborative filtering framework with three metrics: ranking score, Recall and Precision, and demonstrate that it performs better than the commonly used cosine similarity.Comment: 8 pages, 4 figures, 1 tabl

Risk-Averse Matchings over Uncertain Graph Databases

A large number of applications such as querying sensor networks, and analyzing protein-protein interaction (PPI) networks, rely on mining uncertain graph and hypergraph databases. In this work we study the following problem: given an uncertain, weighted (hyper)graph, how can we efficiently find a (hyper)matching with high expected reward, and low risk? This problem naturally arises in the context of several important applications, such as online dating, kidney exchanges, and team formation. We introduce a novel formulation for finding matchings with maximum expected reward and bounded risk under a general model of uncertain weighted (hyper)graphs that we introduce in this work. Our model generalizes probabilistic models used in prior work, and captures both continuous and discrete probability distributions, thus allowing to handle privacy related applications that inject appropriately distributed noise to (hyper)edge weights. Given that our optimization problem is NP-hard, we turn our attention to designing efficient approximation algorithms. For the case of uncertain weighted graphs, we provide a $\frac{1}{3}$-approximation algorithm, and a $\frac{1}{5}$-approximation algorithm with near optimal run time. For the case of uncertain weighted hypergraphs, we provide a $\Omega(\frac{1}{k})$-approximation algorithm, where $k$ is the rank of the hypergraph (i.e., any hyperedge includes at most $k$ nodes), that runs in almost (modulo log factors) linear time. We complement our theoretical results by testing our approximation algorithms on a wide variety of synthetic experiments, where we observe in a controlled setting interesting findings on the trade-off between reward, and risk. We also provide an application of our formulation for providing recommendations of teams that are likely to collaborate, and have high impact.Comment: 25 page