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Network Covalent Solids

Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
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Published on: February 25, 2015

Structure of shells in complex networks.

Jia Shao1, Sergey V Buldyrev, Lidia A Braunstein

  • 1Department of Physics and Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

We analyzed network shell structures to understand transport processes. Our findings reveal two network classes based on connectivity, crucial for network analysis and real-world applications.

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Area of Science:

  • Network science
  • Statistical physics
  • Complex systems analysis

Background:

  • Understanding network structure is vital for analyzing transport processes like information or disease spread.
  • Network shells, defined by distance from a node, are key to studying diffusion dynamics.

Purpose of the Study:

  • To analytically study the statistical properties of network shells around a random node.
  • To develop a method for characterizing correlations within real-world networks.

Main Methods:

  • Analytical derivation of node degree distribution outside shell l.
  • Formulation of an iterative function for the fraction of nodes outside shell l (rl).
  • Introduction of a network correlation function c(rl) to compare empirical and theoretical rl values.

Main Results:

  • Derived analytical expressions for degree distribution and average degree outside shell l.
  • Established an iterative functional form rl=φ(rl-1) based on degree distribution generating functions.
  • Identified two network classes: poorly connected (c(rl)>1) and well-connected (c(rl)<1), differentiating them from random networks.

Conclusions:

  • The derived framework explains power-law distributions in network shells.
  • The network correlation function c(rl) effectively classifies networks based on their connectivity.
  • Findings provide insights into the structural properties of diverse real-world networks.