The Structure of Information Networks

Computer Science 6850
Cornell University
Spring 2011

  • Time: MWF 1:25-2:15 pm.

  • Place: 203 Phillips Hall.


    Course Staff


    The past decade has seen a convergence of social and technological networks, with systems such as the World Wide Web characterized by the interplay between rich information content, the millions of individuals and organizations who create it, and the technology that supports it. This course covers recent research on the structure and analysis of such networks, and on models that abstract their basic properties. Topics include combinatorial and probabilistic techniques for link analysis, centralized and decentralized search algorithms, network models based on random graphs, and connections with work in the social sciences.

    The course prerequisites include introductory-level background in algorithms, graphs, probability, and linear algebra, as well as some basic programming experience (to be able to manipulate network datasets).

    The work for the course will consist primarily of two problem sets, a short reaction paper, and a more substantial project. Coursework should be handed in through CMS.


    Course Outline

    (1) Random Graphs and Small-World Properties

    A major goal of the course is to illustrate how networks across a variety of domains exhibit common structure at a qualitative level. One area in which this arises is in the study of `small-world properties' in networks: many large networks have short paths between most pairs of nodes, even though they are highly clustered at a local level, and they are searchable in the sense that one can navigate to specified target nodes without global knowledge. These properties turn out to provide insight into the structure of large-scale social networks, and, in a different direction, to have applications to the design of decentralized peer-to-peer systems.

    (2) Cascading Behavior in Networks

    We can think of a network as a large circulatory system, through which information continuously flows. This diffusion of information can happen rapidly or slowly; it can be disastrous -- as in a panic or cascading failure -- or beneficial -- as in the spread of an innovation. Work in several areas has proposed models for such processes, and investigated when a network is more or less susceptible to their spread. This type of diffusion or cascade process can also be used as a design principle for network protocols. This leads to the idea of epidemic algorithms, also called gossip-based algorithms, in which information is propagated through a collection of distributed computing hosts, typically using some form of randomization.

    (3) Heavy-Tailed Distributions in Networks

    The degree of a node in a network is the number of neighbors it has. For many large networks -- including the Web, the Internet, collaboration networks, and semantic networks -- the fraction of nodes with very high degrees is much larger than one would expect based on ``standard'' models of random graphs. The particular form of the distribution --- the fraction of nodes with degree d decays like d to some fixed power --- is called a power law. What processes are capable of generating such power laws, and why should they be ubiquitous in large networks? The investigation of these questions suggests that power laws are just one reflection of the local and global processes driving the evolution of these networks.

    (4) Game-Theoretic Models of Behavior in Networks

    In order to model the interaction of agents in a large network, it often makes sense to assume that their behavior is strategic -- that each agent operates so as to optimize his/her/its own self-interest. The study of such systems involves issues at the interface of algorithms and game theory. A central definition here is that of a Nash equilibrium -- a state of the network from which no agent has an incentive to deviate -- and recent work has studied how well a system operates when it is in a Nash equilibrium.

    (5) Spectral Analysis of Networks

    One can gain a lot of insight into the structure of a network by analzing the eigenvalues and eigenvectors of its adjacency matrix. The connection between spectral parameters and the more combinatorial properties of networks and datasets is a subtle issue, and while many results have been established about this connection, it is still not fully understood. This connection has also led to a number of applications, including the development of link analysis algorithms for Web search.

    (6) Clustering and Communities in Networks

    Clustering is one of the oldest and most well-established problems in data analysis; in the context of networks, it can be used to search for densely connected communities. A number of techniques have been applied to this problem, including combinatorial and spectral methods. A task closely related to clustering is the problem of classifying the nodes of a network using a known set of labels. For example, suppose we wanted to classify Web pages into topic categories. Automated text analysis can give us an estimate of the topic of each page; but we also suspect that pages have some tendency to be similar to neighboring pages in the link structure. How should we combine these two sources of evidence? A number of probabilistic frameworks are useful for this task, including the formalism of Markov random fields, which -- for quite different applications -- has been extensively studied in computer vision.