arXiv subjects

Jure Leskovec

Publications and source records attributed to Jure Leskovec.

267 records · Page 15Linked to original sources

arXiv2011

Modeling Social Networks with Node Attributes using the Multiplicative Attribute Graph Model

Networks arising from social, technological and natural domains exhibit rich connectivity patterns and nodes in such networks are often labeled with attributes or features. We address the question of modeling the structure of networks where nodes have attribute information. We present a Multiplicative Attribute Graph (MAG) model that considers nodes with categorical attributes and models the probability of an edge as the product of individual attribute link formation affinities. We develop a scalable variational expectation maximization parameter estimation method. Experiments show that MAG model reliably captures network connectivity as well as provides insights into how different attributes shape the network structure.

cs.SI↗

arXiv2011

Multiplicative Attribute Graph Model of Real-World Networks

Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and especially in social networks, nodes have a rich set of attributes (e.g., age, gender) associated with them. Here we present a model that we refer to as the Multiplicative Attribute Graphs (MAG), which naturally captures the interactions between the network structure and the node attributes. We consider a model where each node has a vector of categorical latent attributes associated with it. The probability of an edge between a pair of nodes then depends on the product of individual attribute-attribute affinities. The model yields itself to mathematical analysis and we derive thresholds for the connectivity and the emergence of the giant connected component, and show that the model gives rise to networks with a constant diameter. We analyze the degree distribution to show that MAG model can produce networks with either log-normal or power-law degree distributions depending on certain conditions.

cs.SI↗

arXiv2011

The Role of Social Networks in Online Shopping: Information Passing, Price of Trust, and Consumer Choice

While social interactions are critical to understanding consumer behavior, the relationship between social and commerce networks has not been explored on a large scale. We analyze Taobao, a Chinese consumer marketplace that is the world's largest e-commerce website. What sets Taobao apart from its competitors is its integrated instant messaging tool, which buyers can use to ask sellers about products or ask other buyers for advice. In our study, we focus on how an individual's commercial transactions are embedded in their social graphs. By studying triads and the directed closure process, we quantify the presence of information passing and gain insights into when different types of links form in the network. Using seller ratings and review information, we then quantify a price of trust. How much will a consumer pay for transaction with a trusted seller? We conclude by modeling this consumer choice problem: if a buyer wishes to purchase a particular product, how does (s)he decide which store to purchase it from? By analyzing the performance of various feature sets in an information retrieval setting, we demonstrate how the social graph factors into understanding consumer behavior.

cs.SI↗

arXiv2010

On the Convexity of Latent Social Network Inference

In many real-world scenarios, it is nearly impossible to collect explicit social network data. In such cases, whole networks must be inferred from underlying observations. Here, we formulate the problem of inferring latent social networks based on network diffusion or disease propagation data. We consider contagions propagating over the edges of an unobserved social network, where we only observe the times when nodes became infected, but not who infected them. Given such node infection times, we then identify the optimal network that best explains the observed data. We present a maximum likelihood approach based on convex programming with a l1-like penalty term that encourages sparsity. Experiments on real and synthetic data reveal that our method near-perfectly recovers the underlying network structure as well as the parameters of the contagion propagation model. Moreover, our approach scales well as it can infer optimal networks of thousands of nodes in a matter of minutes.

cs.SI↗

arXiv2010

Citing for High Impact

The question of citation behavior has always intrigued scientists from various disciplines. While general citation patterns have been widely studied in the literature we develop the notion of citation projection graphs by investigating the citations among the publications that a given paper cites. We investigate how patterns of citations vary between various scientific disciplines and how such patterns reflect the scientific impact of the paper. We find that idiosyncratic citation patterns are characteristic for low impact papers; while narrow, discipline-focused citation patterns are common for medium impact papers. Our results show that crossing-community, or bridging citation patters are high risk and high reward since such patterns are characteristic for both low and high impact papers. Last, we observe that recently citation networks are trending toward more bridging and interdisciplinary forms.

cs.DL↗

arXiv2010

Empirical Comparison of Algorithms for Network Community Detection

Detecting clusters or communities in large real-world graphs such as large social or information networks is a problem of considerable interest. In practice, one typically chooses an objective function that captures the intuition of a network cluster as set of nodes with better internal connectivity than external connectivity, and then one applies approximation algorithms or heuristics to extract sets of nodes that are related to the objective function and that "look like" good communities for the application of interest. In this paper, we explore a range of network community detection methods in order to compare them and to understand their relative performance and the systematic biases in the clusters they identify. We evaluate several common objective functions that are used to formalize the notion of a network community, and we examine several different classes of approximation algorithms that aim to optimize such objective functions. In addition, rather than simply fixing an objective and asking for an approximation to the best cluster of any size, we consider a size-resolved version of the optimization problem. Considering community quality as a function of its size provides a much finer lens with which to examine community detection algorithms, since objective functions and approximation algorithms often have non-obvious size-dependent behavior.

cs.DS↗

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

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↗

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↗

arXiv2008

Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters

A large body of work has been devoted to defining and identifying clusters or communities in social and information networks. We explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions. We employ approximation algorithms for the graph partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities. In particular, we define the network community profile plot, which characterizes the "best" possible community--according to the conductance measure--over a wide range of size scales. We study over 100 large real-world social and information networks. Our results suggest a significantly more refined picture of community structure in large networks than has been appreciated previously. In particular, we observe tight communities that are barely connected to the rest of the network at very small size scales; and communities of larger size scales gradually "blend into" the expander-like core of the network and thus become less "community-like." This behavior is not explained, even at a qualitative level, by any of the commonly-used network generation models. Moreover, it is exactly the opposite of what one would expect based on intuition from expander graphs, low-dimensional or manifold-like graphs, and from small social networks that have served as testbeds of community detection algorithms. We have found that a generative graph model, in which new edges are added via an iterative "forest fire" burning process, is able to produce graphs exhibiting a network community profile plot similar to what we observe in our network datasets.

cs.DS↗

arXiv2008

Planetary-Scale Views on an Instant-Messaging Network

We present a study of anonymized data capturing a month of high-level communication activities within the whole of the Microsoft Messenger instant-messaging system. We examine characteristics and patterns that emerge from the collective dynamics of large numbers of people, rather than the actions and characteristics of individuals. The dataset contains summary properties of 30 billion conversations among 240 million people. From the data, we construct a communication graph with 180 million nodes and 1.3 billion undirected edges, creating the largest social network constructed and analyzed to date. We report on multiple aspects of the dataset and synthesized graph. We find that the graph is well-connected and robust to node removal. We investigate on a planetary-scale the oft-cited report that people are separated by ``six degrees of separation'' and find that the average path length among Messenger users is 6.6. We also find that people tend to communicate more with each other when they have similar age, language, and location, and that cross-gender conversations are both more frequent and of longer duration than conversations with the same gender.

physics.soc-ph↗

arXiv2007

Cascading Behavior in Large Blog Graphs

How do blogs cite and influence each other? How do such links evolve? Does the popularity of old blog posts drop exponentially with time? These are some of the questions that we address in this work. Our goal is to build a model that generates realistic cascades, so that it can help us with link prediction and outlier detection. Blogs (weblogs) have become an important medium of information because of their timely publication, ease of use, and wide availability. In fact, they often make headlines, by discussing and discovering evidence about political events and facts. Often blogs link to one another, creating a publicly available record of how information and influence spreads through an underlying social network. Aggregating links from several blog posts creates a directed graph which we analyze to discover the patterns of information propagation in blogspace, and thereby understand the underlying social network. Not only are blogs interesting on their own merit, but our analysis also sheds light on how rumors, viruses, and ideas propagate over social and computer networks. Here we report some surprising findings of the blog linking and information propagation structure, after we analyzed one of the largest available datasets, with 45,000 blogs and ~ 2.2 million blog-postings. Our analysis also sheds light on how rumors, viruses, and ideas propagate over social and computer networks. We also present a simple model that mimics the spread of information on the blogosphere, and produces information cascades very similar to those found in real life.

physics.soc-ph↗

arXiv2007

The Dynamics of Viral Marketing

We present an analysis of a person-to-person recommendation network, consisting of 4 million people who made 16 million recommendations on half a million products. We observe the propagation of recommendations and the cascade sizes, which we explain by a simple stochastic model. We analyze how user behavior varies within user communities defined by a recommendation network. Product purchases follow a 'long tail' where a significant share of purchases belongs to rarely sold items. We establish how the recommendation network grows over time and how effective it is from the viewpoint of the sender and receiver of the recommendations. While on average recommendations are not very effective at inducing purchases and do not spread very far, we present a model that successfully identifies communities, product and pricing categories for which viral marketing seems to be very effective.

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↗