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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 graphtheoretic 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...
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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.
 Fall '13
 F.Borrelli
 The Aeneid

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