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Nanoscale Systems: Mathematical Modeling, Theory and Applications

Editor-in-Chief: Melnik, Roderick

Managing Editor: Povitsky, Alex

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Nanonetworks: The graph theory framework for modeling nanoscale systems

Jelena Živkovic
  • Department of theoretical physics; Jožef Stefan Institute, Box 3000, SI-1001 Ljubljana Slovenia
  • Scanning Probe Microscopy Group, Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands, EU
  • :
/ Bosiljka Tadic
  • Department of theoretical physics; Jožef Stefan Institute, Box 3000, SI-1001 Ljubljana Slovenia
  • :
Published Online: 2013-02-15 | DOI: https://doi.org/10.2478/nsmmt-2013-0003


Nanonetwork is defined as a mathematical model of nanosize objects with biological, physical and chemical attributes, which are interconnected within certain dynamical process. To demonstrate the potentials of this modeling approach for quantitative study of complexity at nanoscale, in this survey, we consider three kinds of nanonetworks: Genes of a yeast are connected by weighted links corresponding to their coexpression along the cell cycle; Gold nanoparticles, arranged on a substrate, are linked via quantum tunneling junctions which enable single-electron conduction; A network of similar profiles of force–distance curves consists of sequences of states of a molecular complex from HIV–1 virus observed in repeated single-molecule force spectroscopy experiments. The graph-theory analysis of these systems reveals their organizational principles, quantifies the relation between the function of nanostructured materials and their architecture, and helps understand the character of fluctuations at nanoscale.

Keywords: Conducting nanoparticle films; Genetic networks of yeast; Single-molecule force spectroscipy data; Graph theory; Network community detection; Bionanosystems; Viral RNA; Cell; Complex systems

PACS: 62.23.St; 82.37.Rs; 87.18.Cf; 89.75.-k; 89.75.Hc

MSC: 5Cxx; 90B10; 90C35; 92E10; 05C62

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Received: 2012-11-12

Revised: 2013-01-04

Accepted: 2013-01-24

Published Online: 2013-02-15

Citation Information: Nanoscale Systems: Mathematical Modeling, Theory and Applications. Volume 2, Pages 30–48, ISSN (Online) 2299-3290, DOI: https://doi.org/10.2478/nsmmt-2013-0003, February 2013

©2013 Versita Sp. z o.o.. This content is open access.

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