On the Largest Component of a Random Graph with a Subpower-law Degree Sequence in a Subcritical Phase
نویسنده
چکیده
A uniformly random graph on n vertices with a fixed degree sequence, obeying a γ subpower law, is studied. It is shown that, for γ > 3, in a subcritical phase with high probability the largest component size does not exceed nn , εn =O(ln lnn/ lnn), 1/γ being the best power for this random graph. This is similar to the best possible n bound for a different model of the random graph, one with independent vertex degrees, conjectured by Durrett, and proved recently by Janson.
منابع مشابه
The Largest Component in a Subcritical Random Graph with a Power Law Degree Distribution by Svante Janson
It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent γ > 3, the largest component is of order n1/(γ−1). More precisely, the order of the largest component is approximatively given by a simple constant times the largest vertex degree. These results are extended to several other random graph models with power law degree ...
متن کاملThe Largest Component in a Subcritical Random Graph with a Power Law Degree Distribution
It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent γ > 3, the largest component is of order n. More precisely, the order of the largest component is approximatively given by a simple constant times the largest vertex degree. These results are extended to several other random graph models with power law degree distrib...
متن کاملSampling from social networks’s graph based on topological properties and bee colony algorithm
In recent years, the sampling problem in massive graphs of social networks has attracted much attention for fast analyzing a small and good sample instead of a huge network. Many algorithms have been proposed for sampling of social network’ graph. The purpose of these algorithms is to create a sample that is approximately similar to the original network’s graph in terms of properties such as de...
متن کاملThe connected component of the partial duplication graph
We consider the connected component of the partial duplication model for a random graph, a model which was introduced by Bhan, Galas and Dewey as a model for gene expression networks. The most rigorous results are due to Hermann and Pfaffelhuber, who show a phase transition between a subcritical case where in the limit almost all vertices are isolated and a supercritical case where the proporti...
متن کاملCritical behavior in inhomogeneous random graphs
We study the critical behavior of inhomogeneous random graphs where edges are present independently but with unequal edge occupation probabilities. We show that the critical behavior depends sensitively on the properties of the asymptotic degrees. Indeed, when the proportion of vertices with degree at least k is bounded above by k−τ+1 for some τ > 4, the largest critical connected component is ...
متن کامل