Distinguishing Power-Law Uniform Random Graphs from Inhomogeneous Random Graphs Through Small Subgraphs

DISTINGUISHING VERTICES OF INHOMOGENEOUS RANDOM GRAPHS By

We explore under what conditions simple combinatorial attributes and algorithms such as the distance sequence and degree-based partitioning and refinement can be used to distinguish vertices of inhomogeneous random graphs. In the classical setting of Erdős-Renyi graphs and random regular graphs it has been proven that vertices can be distinguished in a constant number of rounds of degree-based ...

Uniform generation of random graphs with power-law degree sequences

We give a linear-time algorithm that approximately uniformly generates a randomsimple graph with a power-law degree sequence whose exponent is at least 2.8811.While sampling graphs with power-law degree sequence of exponent at least 3 is fairlyeasy, and many samplers work efficiently in this case, the problem becomes dramaticallymore difficult when the exponent drops below 3; ou...

On small subgraphs of random graphs

Small subgraphs of random regular graphs

The main aim of this short paper is to answer the following question. Given a fixed graph H , for which values of the degree d does a random d-regular graph on n vertices contain a copy of H with probability close to one?

Finding induced subgraphs in scale-free inhomogeneous random graphs

We study the induced subgraph isomorphism problem on inhomogeneous random graphs with infinite variance power-law degrees. We provide a fast algorithm that determines for any connected graph H on k vertices if it exists as induced subgraph in a random graph with n vertices. By exploiting the scale-free graph structure, the algorithm runs in O(ne 4 ) time, and finds for constant k an instance of...