Discrete Scale Invariance in Scale Free Graphs
Mat\'ias Gra\~na, Juan Pablo Pinasco
TL;DR
This paper investigates the presence of discrete scale invariance in scale-free graphs, revealing hierarchical structures through energy distribution patterns and log periodic oscillations.
Contribution
It introduces an energy function to analyze scale-free graphs, uncovering fractal patterns and hierarchical degree distributions not previously characterized.
Findings
Energy distribution exhibits fractal patterns.
Log periodic oscillations indicate discrete scale invariance.
Hierarchical node degree distribution observed.
Abstract
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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