Nanonetworks: the graph theory framework for modeling nanoscale systems.

*(English)*Zbl 1272.05211Summary: A nanonetwork is defined as a mathematical model of nanosize objects with biological, physical and chemical attributes, which are interconnected within certain dynamical processes. To demonstrate the potentials of this modeling approach for the 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, 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.

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.

##### MSC:

05C90 | Applications of graph theory |

90B10 | Deterministic network models in operations research |

90C35 | Programming involving graphs or networks |

92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |

05C62 | Graph representations (geometric and intersection representations, etc.) |

##### Keywords:

conducting nanoparticle films; genetic networks of yeast; single-molecule force spectroscipy data; graph theory; network community detection; bionanosystems; viral RNA; cell; complex systems##### Software:

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\textit{J. Živković} and \textit{B. Tadić}, Nanoscale Syst., Math. Model. Theory Appl. 2, 30--48 (2013; Zbl 1272.05211)

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