ArticleScientific reports2017
The exact Laplacian spectrum for the Dyson hierarchical network.
Article in Scientific reports, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Dynamics of a Polymer Network Modeled by a Fractal Cactus.Polymers · 2018Article
- Relaxation dynamics of generalized scale-free polymer networks.Scientific reports · 2018Article
- Dynamics of Dual Scale-Free Polymer Networks.Polymers · 2017Article
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Authors and funding
2 authors.
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Abstract
We consider the Dyson hierarchical graph , that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter σ ∈ (1/2, 1]. Exploiting the deterministic recursivity through which is built, we are able to derive explicitly the whole set of the eigenvalues and the eigenvectors for its Laplacian matrix. Given that the Laplacian operator is intrinsically implied in the analysis of dynamic processes (e.g., random walks) occurring on the graph, as well as in the investigation of the dynamical properties of connected structures themselves (e.g., vibrational structures and relaxation modes), this result allows addressing analytically a large class of problems. In particular, as examples of applications, we study the random walk and the continuous-time quantum walk embedded in , the relaxation times of a polymer whose structure is described by , and the community structure of in terms of modularity measures.
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