Jon M. Kleinberg

Authoritative sources in a hyperlinked environment

The network structure of a hyperlinked environment can be a rich source of information about the content of the environment, provided we have effective means for understanding it. We develop a set of algorithmic tools for extracting information from the link structures of such environments, and report on experiments that demonstrate their effectiveness in a variety of context on the World Wide Web. The central issue we address within our framework is the distillation of broad search topics, through the discovery of “authorative” information sources on such topics. We propose and test an algorithmic formulation of the notion of authority, based on the relationship between a set of relevant authoritative pages and the set of “hub pages” that join them together in the link structure. Our formulation has connections to the eigenvectors of certain matrices associated with the link graph; these connections in turn motivate additional heuristrics for link-based analysis.

The small-world phenomenon: an algorithmic perspective

A method of improving certain characteristics of cadmium mercury telluride single crystal material by heat treating the single crystal material in the presence of both tellurium and mercury.

Group formation in large social networks: membership, growth, and evolution

The processes by which communities come together, attract new members, and develop over time is a central research issue in the social sciences - political movements, professional organizations, and religious denominations all provide fundamental examples of such communities. In the digital domain, on-line groups are becoming increasingly prominent due to the growth of community and social networking sites such as MySpace and LiveJournal. However, the challenge of collecting and analyzing large-scale time-resolved data on social groups and communities has left most basic questions about the evolution of such groups largely unresolved: what are the structural features that influence whether individuals will join communities, which communities will grow rapidly, and how do the overlaps among pairs of communities change over time.Here we address these questions using two large sources of data: friendship links and community membership on LiveJournal, and co-authorship and conference publications in DBLP. Both of these datasets provide explicit user-defined communities, where conferences serve as proxies for communities in DBLP. We study how the evolution of these communities relates to properties such as the structure of the underlying social networks. We find that the propensity of individuals to join communities, and of communities to grow rapidly, depends in subtle ways on the underlying network structure. For example, the tendency of an individual to join a community is influenced not just by the number of friends he or she has within the community, but also crucially by how those friends are connected to one another. We use decision-tree techniques to identify the most significant structural determinants of these properties. We also develop a novel methodology for measuring movement of individuals between communities, and show how such movements are closely aligned with changes in the topics of interest within the communities.

Navigation in a small world

The small-world phenomenon — the principle that most of us are linked by short chains of acquaintances — was first investigated as a question in sociology and is a feature of a range of networks arising in nature and technology. Experimental study of the phenomenon revealed that it has two fundamental components: first, such short chains are ubiquitous, and second, individuals operating with purely local information are very adept at finding these chains. The first issue has been analysed, and here I investigate the second by modelling how individuals can find short chains in a large social network.

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 superlinearly 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. Last, we analyze the connection between the temporal evolution of the degree distribution and densification of a graph. We find that the two are fundamentally related. We also observe that real networks exhibit this type of relation between densification and the degree distribution.

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.

The web as a graph: measurements, models, and methods

The pages and hyperlinks of the World-Wide Web may be viewed as nodes and edges in a directed graph. This graph is a fascinating object of study: it has several hundred million nodes today, over a billion links, and appears to grow exponentially with time. There are many reasons -- mathematical, sociological, and commercial -- for studying the evolution of this graph. In this paper we begin by describing two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery. We then report a number of measurements and properties of this graph that manifested themselves as we ran these algorithms on the Web. Finally, we observe that traditional random graph models do not explain these observations, and we propose a new family of random graph models. These models point to a rich new sub-field of the study of random graphs, and raise questions about the analysis of graph algorithms on the Web.

Inferring Web communities from link topology

The World Wide Web grows through a decentralized, almost anarchic process, and this has resulted in a large hyperlinked corpus without the kind of logical organization that can be built into more tradit,ionally-created hypermedia. To extract, meaningful structure under such circumstances, we develop a notion of hyperlinked communities on the www t,hrough an analysis of the link topology. By invoking a simple, mathematically clean method for defining and exposing the structure of these communities, we are able to derive a number of themes: The communities can be viewed as containing a core of central, “authoritative” pages linked togh and they exhibit a natural type of hierarchical topic generalization that can be inferred directly from the pat,t,ern of linkage. Our investigation shows that although the process by which users of the Web create pages and links is very difficult to understand at a “local” level, it results in a much greater degree of orderly high-level structure than has typically been assumed.

Automatic resource compilation by analyzing hyperlink structure and associated text

We describe the design, prototyping and evaluation of ARC, a system for automatically compiling a list of authoritative Web resources on any (sufficiently broad) topic. The goal of ARC is to compile resource lists similar to those provided by Yahoo! or Infoseek. The fundamental difference is that these services construct lists either manually or through a combination of human and automated effort, while ARC operates fully automatically. We describe the evaluation of ARC, Yahoo!, and Infoseek resource lists by a panel of human users. This evaluation suggests that the resources found by ARC frequently fare almost as well as, and sometimes better than, lists of resources that are manually compiled or classified into a topic. We also provide examples of ARC resource lists for the reader to examine.

Mapping the world's photos

We investigate how to organize a large collection of geotagged photos, working with a dataset of about 35 million images collected from Flickr. Our approach combines content analysis based on text tags and image data with structural analysis based on geospatial data. We use the spatial distribution of where people take photos to define a relational structure between the photos that are taken at popular places. We then study the interplay between this structure and the content, using classification methods for predicting such locations from visual, textual and temporal features of the photos. We find that visual and temporal features improve the ability to estimate the location of a photo, compared to using just textual features. We illustrate using these techniques to organize a large photo collection, while also revealing various interesting properties about popular cities and landmarks at a global scale.