Course material (slides and videos) can be found on
CMS.
Course Staff
Overview
This is a seminar focusing on models for networks and for some of the fundamental processes that take place within them. Topics will include the small-world phenomenon, decentralized search, contagion, cascading behavior, graph partitioning, and spectral analysis.
The seminar is structured as a 2-credit S/U-only class at the 7000-level,
and in keeping with this format the classwork will consist of
lecture participation and supplementary reading of papers, but no
graded material.
Course Outline
(1) 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 an epidemic disease 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.
- Simple Probabilistic Models of Contagion.
- Models of Collective Action.
- Threshold-Based Models of Diffusion in Networks.
- Finding Influential Sets of Nodes.
(2) Small-World Phenomena in Networks
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.
- Small-world experiments in social networks.
- Basic Random Graph Models, and the Consequences of Expansion.
- Decentralized Search in Networks.
- Decentralized Search in Peer-to-Peer Systems
- Nearest-Neighbor Search in Metric Spaces
(3) 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.
- Link Analysis and Web Search