Effect on normalized graph Laplacian spectrum by motif attachment and duplication
نویسندگان
چکیده
منابع مشابه
Effect on normalized graph Laplacian spectrum by motif attachment and duplication
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 has been obse...
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Here we investigate how the spectrum of the normalized graph Laplacian gets affected by certain graph operations like motif duplication and graph (or motif) joining.
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The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this spectrum under local and global operations like motif doubling, graph joining or splitting. The eigenvalue 1 plays a particular role, and we therefore emphasize tho...
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Let $G$ be a graph without an isolated vertex, the normalized Laplacian matrix $tilde{mathcal{L}}(G)$ is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$, where $mathcal{D}$ is a diagonal matrix whose entries are degree of vertices of $G$. The eigenvalues of $tilde{mathcal{L}}(G)$ are called as the normalized Laplacian eigenva...
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let $g$ be a graph without an isolated vertex, the normalized laplacian matrix $tilde{mathcal{l}}(g)$is defined as $tilde{mathcal{l}}(g)=mathcal{d}^{-frac{1}{2}}mathcal{l}(g) mathcal{d}^{-frac{1}{2}}$, where $mathcal{d}$ is a diagonal matrix whose entries are degree of vertices of $g$. the eigenvalues of$tilde{mathcal{l}}(g)$ are called as the normalized laplacian ...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2015
ISSN: 0096-3003
DOI: 10.1016/j.amc.2015.03.118