arXiv subjects

Jon Kleinberg

Publications and source records attributed to Jon Kleinberg.

160 records · Page 9Linked to original sources

arXiv2013

Subgraph Frequencies: Mapping the Empirical and Extremal Geography of Large Graph Collections

A growing set of on-line applications are generating data that can be viewed as very large collections of small, dense social graphs -- these range from sets of social groups, events, or collaboration projects to the vast collection of graph neighborhoods in large social networks. A natural question is how to usefully define a domain-independent coordinate system for such a collection of graphs, so that the set of possible structures can be compactly represented and understood within a common space. In this work, we draw on the theory of graph homomorphisms to formulate and analyze such a representation, based on computing the frequencies of small induced subgraphs within each graph. We find that the space of subgraph frequencies is governed both by its combinatorial properties, based on extremal results that constrain all graphs, as well as by its empirical properties, manifested in the way that real social graphs appear to lie near a simple one-dimensional curve through this space. We develop flexible frameworks for studying each of these aspects. For capturing empirical properties, we characterize a simple stochastic generative model, a single-parameter extension of Erdos-Renyi random graphs, whose stationary distribution over subgraphs closely tracks the concentration of the real social graph families. For the extremal properties, we develop a tractable linear program for bounding the feasible space of subgraph frequencies by harnessing a toolkit of known extremal graph theory. Together, these two complementary frameworks shed light on a fundamental question pertaining to social graphs: what properties of social graphs are 'social' properties and what properties are 'graph' properties? We conclude with a brief demonstration of how the coordinate system we examine can also be used to perform classification tasks, distinguishing between social graphs of different origins.

cs.SI↗

arXiv2013

On Discrete Preferences and Coordination

An active line of research has considered games played on networks in which payoffs depend on both a player's individual decision and also the decisions of her neighbors. Such games have been used to model issues including the formation of opinions and the adoption of technology. A basic question that has remained largely open in this area is to consider games where the strategies available to the players come from a fixed, discrete set, and where players may have different intrinsic preferences among the possible strategies. It is natural to model the tension among these different preferences by positing a distance function on the strategy set that determines a notion of "similarity" among strategies; a player's payoff is determined by the distance from her chosen strategy to her preferred strategy and to the strategies chosen by her network neighbors. Even when there are only two strategies available, this framework already leads to natural open questions about a version of the classical Battle of the Sexes problem played on a graph. We develop a set of techniques for analyzing this class of games, which we refer to as discrete preference games. We parametrize the games by the relative extent to which a player takes into account the effect of her preferred strategy and the effect of her neighbors' strategies, allowing us to interpolate between network coordination games and unilateral decision-making. When these two effects are balanced, we show that the price of stability is equal to 1 for any discrete preference game in which the distance function on the strategies is a tree metric; as a special case, this includes the Battle of the Sexes on a graph. We also show that trees form the maximal family of metrics for which the price of stability is 1, and produce a collection of metrics on which the price of stability converges to a tight bound of 2.

cs.GT↗

arXiv2013

Characterizing and curating conversation threads: Expansion, focus, volume, re-entry

Discussion threads form a central part of the experience on many Web sites, including social networking sites such as Facebook and Google Plus and knowledge creation sites such as Wikipedia. To help users manage the challenge of allocating their attention among the discussions that are relevant to them, there has been a growing need for the algorithmic curation of on-line conversations --- the development of automated methods to select a subset of discussions to present to a user. Here we consider two key sub-problems inherent in conversational curation: length prediction --- predicting the number of comments a discussion thread will receive --- and the novel task of re-entry prediction --- predicting whether a user who has participated in a thread will later contribute another comment to it. The first of these sub-problems arises in estimating how interesting a thread is, in the sense of generating a lot of conversation; the second can help determine whether users should be kept notified of the progress of a thread to which they have already contributed. We develop and evaluate a range of approaches for these tasks, based on an analysis of the network structure and arrival pattern among the participants, as well as a novel dichotomy in the structure of long threads. We find that for both tasks, learning-based approaches using these sources of information yield improvements for all the performance metrics we used.

cs.SI↗

arXiv2012

You had me at hello: How phrasing affects memorability

Understanding the ways in which information achieves widespread public awareness is a research question of significant interest. We consider whether, and how, the way in which the information is phrased --- the choice of words and sentence structure --- can affect this process. To this end, we develop an analysis framework and build a corpus of movie quotes, annotated with memorability information, in which we are able to control for both the speaker and the setting of the quotes. We find that there are significant differences between memorable and non-memorable quotes in several key dimensions, even after controlling for situational and contextual factors. One is lexical distinctiveness: in aggregate, memorable quotes use less common word choices, but at the same time are built upon a scaffolding of common syntactic patterns. Another is that memorable quotes tend to be more general in ways that make them easy to apply in new contexts --- that is, more portable. We also show how the concept of "memorable language" can be extended across domains.

cs.CL↗

arXiv2012

Echoes of power: Language effects and power differences in social interaction

Understanding social interaction within groups is key to analyzing online communities. Most current work focuses on structural properties: who talks to whom, and how such interactions form larger network structures. The interactions themselves, however, generally take place in the form of natural language --- either spoken or written --- and one could reasonably suppose that signals manifested in language might also provide information about roles, status, and other aspects of the group's dynamics. To date, however, finding such domain-independent language-based signals has been a challenge. Here, we show that in group discussions power differentials between participants are subtly revealed by how much one individual immediately echoes the linguistic style of the person they are responding to. Starting from this observation, we propose an analysis framework based on linguistic coordination that can be used to shed light on power relationships and that works consistently across multiple types of power --- including a more "static" form of power based on status differences, and a more "situational" form of power in which one individual experiences a type of dependence on another. Using this framework, we study how conversational behavior can reveal power relationships in two very different settings: discussions among Wikipedians and arguments before the U.S. Supreme Court.

cs.SI↗

arXiv2012

How Bad is Forming Your Own Opinion?

The question of how people form their opinion has fascinated economists and sociologists for quite some time. In many of the models, a group of people in a social network, each holding a numerical opinion, arrive at a shared opinion through repeated averaging with their neighbors in the network. Motivated by the observation that consensus is rarely reached in real opinion dynamics, we study a related sociological model in which individuals' intrinsic beliefs counterbalance the averaging process and yield a diversity of opinions. By interpreting the repeated averaging as best-response dynamics in an underlying game with natural payoffs, and the limit of the process as an equilibrium, we are able to study the cost of disagreement in these models relative to a social optimum. We provide a tight bound on the cost at equilibrium relative to the optimum; our analysis draws a connection between these agreement models and extremal problems that lead to generalized eigenvalues. We also consider a natural network design problem in this setting: which links can we add to the underlying network to reduce the cost of disagreement at equilibrium?

cs.GT↗

arXiv2011

Voting with Limited Information and Many Alternatives

The traditional axiomatic approach to voting is motivated by the problem of reconciling differences in subjective preferences. In contrast, a dominant line of work in the theory of voting over the past 15 years has considered a different kind of scenario, also fundamental to voting, in which there is a genuinely "best" outcome that voters would agree on if they only had enough information. This type of scenario has its roots in the classical Condorcet Jury Theorem; it includes cases such as jurors in a criminal trial who all want to reach the correct verdict but disagree in their inferences from the available evidence, or a corporate board of directors who all want to improve the company's revenue, but who have different information that favors different options. This style of voting leads to a natural set of questions: each voter has a {\em private signal} that provides probabilistic information about which option is best, and a central question is whether a simple plurality voting system, which tabulates votes for different options, can cause the group decision to arrive at the correct option. We show that plurality voting is powerful enough to achieve this: there is a way for voters to map their signals into votes for options in such a way that --- with sufficiently many voters --- the correct option receives the greatest number of votes with high probability. We show further, however, that any process for achieving this is inherently expensive in the number of voters it requires: succeeding in identifying the correct option with probability at least $1 - η$ requires $Ω(n^3 ε^{-2} \log η^{-1})$ voters, where $n$ is the number of options and $ε$ is a distributional measure of the minimum difference between the options.

cs.DM↗

arXiv2010

Governance in Social Media: A case study of the Wikipedia promotion process

Social media sites are often guided by a core group of committed users engaged in various forms of governance. A crucial aspect of this type of governance is deliberation, in which such a group reaches decisions on issues of importance to the site. Despite its crucial --- though subtle --- role in how a number of prominent social media sites function, there has been relatively little investigation of the deliberative aspects of social media governance. Here we explore this issue, investigating a particular deliberative process that is extensive, public, and recorded: the promotion of Wikipedia admins, which is determined by elections that engage committed members of the Wikipedia community. We find that the group decision-making at the heart of this process exhibits several fundamental forms of relative assessment. First we observe that the chance that a voter will support a candidate is strongly dependent on the relationship between characteristics of the voter and the candidate. Second we investigate how both individual voter decisions and overall election outcomes can be based on models that take into account the sequential, public nature of the voting.

physics.soc-ph↗

arXiv2010

The Directed Closure Process in Hybrid Social-Information Networks, with an Analysis of Link Formation on Twitter

It has often been taken as a working assumption that directed links in information networks are frequently formed by "short-cutting" a two-step path between the source and the destination -- a kind of implicit "link copying" analogous to the process of triadic closure in social networks. Despite the role of this assumption in theoretical models such as preferential attachment, it has received very little direct empirical investigation. Here we develop a formalization and methodology for studying this type of directed closure process, and we provide evidence for its important role in the formation of links on Twitter. We then analyze a sequence of models designed to capture the structural phenomena related to directed closure that we observe in the Twitter data.

stat.ML↗

arXiv2010

Signed Networks in Social Media

Relations between users on social media sites often reflect a mixture of positive (friendly) and negative (antagonistic) interactions. In contrast to the bulk of research on social networks that has focused almost exclusively on positive interpretations of links between people, we study how the interplay between positive and negative relationships affects the structure of on-line social networks. We connect our analyses to theories of signed networks from social psychology. We find that the classical theory of structural balance tends to capture certain common patterns of interaction, but that it is also at odds with some of the fundamental phenomena we observe --- particularly related to the evolving, directed nature of these on-line networks. We then develop an alternate theory of status that better explains the observed edge signs and provides insights into the underlying social mechanisms. Our work provides one of the first large-scale evaluations of theories of signed networks using on-line datasets, as well as providing a perspective for reasoning about social media sites.

physics.soc-ph↗

arXiv2010

Predicting Positive and Negative Links in Online Social Networks

We study online social networks in which relationships can be either positive (indicating relations such as friendship) or negative (indicating relations such as opposition or antagonism). Such a mix of positive and negative links arise in a variety of online settings; we study datasets from Epinions, Slashdot and Wikipedia. We find that the signs of links in the underlying social networks can be predicted with high accuracy, using models that generalize across this diverse range of sites. These models provide insight into some of the fundamental principles that drive the formation of signed links in networks, shedding light on theories of balance and status from social psychology; they also suggest social computing applications by which the attitude of one user toward another can be estimated from evidence provided by their relationships with other members of the surrounding social network.

physics.soc-ph↗

arXiv2010

Information-Sharing and Privacy in Social Networks

We present a new model for reasoning about the way information is shared among friends in a social network, and the resulting ways in which it spreads. Our model formalizes the intuition that revealing personal information in social settings involves a trade-off between the benefits of sharing information with friends, and the risks that additional gossiping will propagate it to people with whom one is not on friendly terms. We study the behavior of rational agents in such a situation, and we characterize the existence and computability of stable information-sharing networks, in which agents do not have an incentive to change the partners with whom they share information. We analyze the implications of these stable networks for social welfare, and the resulting fragmentation of the social network.

cs.GT↗

arXiv2009

Kronecker Graphs: An Approach to Modeling Networks

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization.

stat.ML↗

arXiv2009

How opinions are received by online communities: A case study on Amazon.com helpfulness votes

There are many on-line settings in which users publicly express opinions. A number of these offer mechanisms for other users to evaluate these opinions; a canonical example is Amazon.com, where reviews come with annotations like "26 of 32 people found the following review helpful." Opinion evaluation appears in many off-line settings as well, including market research and political campaigns. Reasoning about the evaluation of an opinion is fundamentally different from reasoning about the opinion itself: rather than asking, "What did Y think of X?", we are asking, "What did Z think of Y's opinion of X?" Here we develop a framework for analyzing and modeling opinion evaluation, using a large-scale collection of Amazon book reviews as a dataset. We find that the perceived helpfulness of a review depends not just on its content but also but also in subtle ways on how the expressed evaluation relates to other evaluations of the same product. As part of our approach, we develop novel methods that take advantage of the phenomenon of review "plagiarism" to control for the effects of text in opinion evaluation, and we provide a simple and natural mathematical model consistent with our findings. Our analysis also allows us to distinguish among the predictions of competing theories from sociology and social psychology, and to discover unexpected differences in the collective opinion-evaluation behavior of user populations from different countries.

cs.CL↗

arXiv2008

The Structure of Information Pathways in a Social Communication Network

Social networks are of interest to researchers in part because they are thought to mediate the flow of information in communities and organizations. Here we study the temporal dynamics of communication using on-line data, including e-mail communication among the faculty and staff of a large university over a two-year period. We formulate a temporal notion of "distance" in the underlying social network by measuring the minimum time required for information to spread from one node to another -- a concept that draws on the notion of vector-clocks from the study of distributed computing systems. We find that such temporal measures provide structural insights that are not apparent from analyses of the pure social network topology. In particular, we define the network backbone to be the subgraph consisting of edges on which information has the potential to flow the quickest. We find that the backbone is a sparse graph with a concentration of both highly embedded edges and long-range bridges -- a finding that sheds new light on the relationship between tie strength and connectivity in social networks.

physics.soc-ph↗

arXiv2007

Graph Evolution: Densification and Shrinking Diameters

How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? 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 super-linearly 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.

physics.soc-ph↗