arXiv subjects

Jefferson Elbert Simões

Publications and source records attributed to Jefferson Elbert Simões.

2 recordsLinked to original sources

arXiv2017

Power-law decay of the degree-sequence probabilities of multiple random graphs with application to graph isomorphism

We consider events over the probability space generated by the degree sequences of multiple independent Erdős-Rényi random graphs, and consider an approximation probability space where such degree sequences are deemed to be sequences of i.i.d. random variables. We show that, for any sequence of events with probabilities asymptotically smaller than some power law in the approximation model, the same upper bound also holds in the original model. We accomplish this by extending an approximation framework proposed in a seminal paper by McKay and Wormald. Finally, as an example, we apply the developed framework to bound the probability of isomorphism-related events over multiple independent random graphs.

math.PR↗

arXiv2016

Local symmetry in random graphs

Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their automorphism groups, which do not account for the similarity of local structures. We introduce the concept of local symmetry, which reflects the structural equivalence of the vertices' egonets. We study the emergence of asymmetry in the Erdős-Rényi random graph model and identify regimes of both asymptotic local symmetry and asymptotic local asymmetry. We find that local symmetry persists at least to an average degree of $n^{1/3}$ and local asymmetry emerges at an average degree not greater than $n^{1/2}$, which are regimes of much larger average degree than for traditional, global asymmetry.

math.PR↗