Effect on normalized graph Laplacian spectrum by motif attachment and duplication

Ranjit Mehatari and Anirban Banerjee

Applied Mathematics and Computation, 2015, vol. 261, issue C, 382-387

Abstract: To some extent, graph evolutionary mechanisms can be explained by its spectra. Here, we are interested in two graph operations, namely, motif (subgraph) doubling and attachment that are biologically relevant. We investigate how these two processes affect the spectrum of the normalized graph Laplacian. A high (algebraic) multiplicity of the eigenvalues 1,1±0.5,1±0.5 and others have been observed in the spectrum of many real networks. We attempt to explain the production of distinct eigenvalues by motif doubling and attachment. Results on the eigenvalue 1 are discussed separately.

Keywords: Normalized graph Laplacian; Graph spectrum; Eigenvalue 1; Motif doubling; Motif attachment (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:261:y:2015:i:c:p:382-387

DOI: 10.1016/j.amc.2015.03.118

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