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Random Networks, Graphs, and Matrices
Author(s) -
Eichinger B. E.
Publication year - 2007
Publication title -
macromolecular symposia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.257
H-Index - 76
eISSN - 1521-3900
pISSN - 1022-1360
DOI - 10.1002/masy.200751003
Subject(s) - eigenvalues and eigenvectors , random graph , elasticity (physics) , mathematics , random matrix , statistical physics , tensor (intrinsic definition) , combinatorics , physics , pure mathematics , graph , quantum mechanics , thermodynamics
Summary: The theory of elasticity based on the distribution function of the gyration tensor is reviewed. It is shown that the James‐Guth potential for a network is a model potential of mean force, derivable in principle from the true many‐body potential for the elastic body. The determination of the modulus of elasticity is resolved in the calculation of the statistical mechanical average of the smallest, non‐zero, eigenvalue of the connectivity matrix that describes the network. The mathematical problem to determine the spectrum of eigenvalues of the random network can be couched in both the language of random graphs and of random matrices.