CS 6824: Hypergraph Algorithms and Applications
Spring 2014
T. M. Murali

Analysis of networks is ubiquitous in modern science, engineering, and
the humanities.  An overwhelming majority of these approaches use
directed or undirected graphs in which edges connect pairs of nodes.
However pair-wise interactions cannot accurately represent the manifold
phenomena that involve coordinated activity of assemblages of more than
two entities, e.g., a protein complex that acts as a unit or social
interactions that occur among the members of a group such as a family or
a criminal gang. 

Hypergraphs are emerging as an attractive alternative to graphs to
represent such phenomena. Informally, a hyperedge (an edge in a
hypergraph) is simply a connection among two or more nodes. Although
hypegraph theory is a well-established area of mathematics, application
of these concepts is relatively rare in network science. This course
will discuss hypergraph theory, algorithms, and applications to answer
the following questions:

* How do hypergraphs arise in different domains? Molecular biology is an
  especially fertile source.

* What are appropriate ways to represent hypergraphs mathematically and
  computationally?

* How do we solve basic algorithmic problems on hypergaphs? Examples
  include shortest paths, random walks, and network flows.

* Can we reverse engineer hypergraphs from existing graph databases?

* How can we reinterpret datasets in areas such as molecular biology and
  social network through the lens of hypergraphs?

Lectures, student presentations, and research projects will drive the
course. A regularly-updated list of papers that we may discuss is
available at http://www.citeulike.org/user/tmmurali/tag/2014-spring-cs6824-hypergraphs

Pre-requisites: Graduate work in algorithms, machine learning, or data
mining will be very useful. Ability to program in a language such as
Python, Matlab, or C++ is very important.