arXiv subjects

Matías Graña

Publications and source records attributed to Matías Graña.

2 recordsLinked to original sources

arXiv2006

Discrete Scale Invariance in Scale Free Graphs

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.

cond-mat.dis-nn↗

arXiv2006

Condition numbers and scale free graphs

In this work we study the condition number of the least square matrix corresponding to scale free networks. We compute a theoretical lower bound of the condition number which proves that they are ill conditioned. Also, we analyze several matrices from networks generated with the linear preferential attachment model showing that it is very difficult to compute the power law exponent by the least square method due to the severe lost of accuracy expected from the corresponding condition numbers.

cond-mat.dis-nn↗