Defining dimension of a complex network. (English) Zbl 1119.82015
Summary: An important question in statistical mechanics is the dependence of model behavior on the dimension of the system. In this paper, we discuss extending the definition of dimension from regular lattices to complex networks. We use the definition to study how the extensive property of the power law potential exponent depends on dimension.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 94C05 | Analytic circuit theory |
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