Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ess of computer networks. Though not relevant for the rest of the problem, we mention a few other examples of how the algebraic connectivity can be used. These results, which relate graph-theoretic properties of G to properties of the spectrum of L, belong to a field called spectral graph theory. For example, λ2 > 0 if and only if the graph is connected. The eigenvector v2 associated with λ2 is often called the Fiedler vector and is widely used in a graph partitioning technique called spectral partitioning, which assigns nodes to one of two groups based on the sign of the relevant component in v2 . Finally, λ2 is also closely related to a quantity called the isoperimetric number or Cheeger constant of G, which measures the degree to which a graph has a bottleneck. The problem is to choose the edge weights w ∈ Rm , subject to some linear inequalities (and the + nonnegativity constraint) so as to maximize the algebraic connectivity: maximize λ2 subject to w 0, Fw g, with variable w ∈ Rm . The problem data are A (which gives the graph topology), and F and g (which describe the constraints on the weights). 133 (a) Describe how to solve this problem using conve...
View Full Document

This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

Ask a homework question - tutors are online