Discrete Scale Invariance in Scale Free Graphs

Details Discrete Scale Invariance in Scale Free Graphs Discrete Scale Invariance in Scale Free Graphs

2006-02-14

arxiv.org/abs/cond-mat/0602337v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

13 pages, 12 figures

Scientific paper

10.1016/j.physa.2007.02.047

In this work we introduce an energy function in order to study finite scale free graphs generated with different models. The energy distribution has a fractal pattern and presents log periodic oscillations for high energies. This oscillations are related to a discrete scale invariance of certain graphs, that is, there are preferred scaling ratios suggesting a hierarchical distribution of node degrees. On the other hand, small energies correspond to graphs with evenly distributed degrees.

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