NDLI: Convex graph invariants

Content Provider	IEEE Xplore Digital Library
Author	Chandrasekaran, V. Parrilo, P.A. Willsky, A.S.
Copyright Year	2012
Description	Author affiliation: Massachusetts Institute of Technology, USA (Chandrasekaran, V.; Parrilo, P.A.; Willsky, A.S.)
Abstract	The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants that are convex functions of the adjacency matrix of a graph. Some examples include functions of a graph such as the maximum degree, the MAXCUT value (and its semidefinite relaxation), and spectral invariants such as the sum of the k largest eigenvalues. Such functions can be used to construct convex sets that impose various structural constraints on graphs, and thus provide a unified framework for solving a number of interesting graph problems via convex optimization. We give a representation of all convex graph invariants in terms of certain elementary invariants, and we describe methods to compute or approximate convex graph invariants tractably. We discuss the interesting subclass of spectral invariants, and also compare convex and non-convex invariants. Finally we use convex graph invariants to provide efficient convex programming solutions to graph problems such as the deconvolution of the composition of two graphs into the individual components, hypothesis testing between graph families, and the generation of graphs with certain desired structural properties.
Starting Page	1
Ending Page	6
File Size	241075
Page Count	6
File Format	PDF
ISBN	9781467331395
e-ISBN	9781467331401
e-ISBN	9781467331388
DOI	10.1109/CISS.2012.6310764
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-03-21
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Symmetric matrices Tin Programming Convex functions Eigenvalues and eigenfunctions Approximation methods Labeling
Content Type	Text
Resource Type	Article

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