Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0808.0509

Evolving Clustered Random Networks

Shweta Bansal·Shashank Khandelwal·Lauren Ancel Meyers
View original source ↗Read source document ↗Export metadata ↓

Abstract

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as generic models for studying the impacts of degree distributions and clustering on dynamical processes as well as null models for detecting other structural properties in empirical networks.

Explore related subjects

cs.DMphysics.soc-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shweta Bansal, Shashank Khandelwal, Lauren Ancel Meyers. 2008-08-04. Evolving Clustered Random Networks. https://doi.org/10.1186/1471-2105-10-405

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces

In symbolic dynamics, the fixed-point construction from arXiv:0910.2415 defines shift spaces of finite type whose configurations embed infinite hierarchies of tilings. This article provides a "black box" abstraction of this method phrased in terms of substitutions and $S$-adic limit spaces operating over sequences of increasingly large alphabets. By quantifying the amount of information computed by the substitutions at each level, and using a suitable parallel model of computation, we provide a simple positive criterion of multidimensional soficity that generalizes classical examples from the literature.

cs.DM↗
arXiv2026

Flip Dynamics for Sampling Colorings: Improving $(11/6-ε)$ Using a Simple Metric

We present improved bounds for randomly sampling $k$-colorings of graphs with maximum degree $Δ$; our results hold without any further structural assumptions on the graph. The Glauber dynamics is a simple single-site update Markov chain. Jerrum (1995) proved an optimal $O(n\log{n})$ mixing-time bound for Glauber dynamics whenever $k>2Δ$ where $Δ$ is the maximum degree of the input graph. This bound was improved by Vigoda (1999) to $k>(11/6)Δ$ using a "flip" dynamics which recolors (small) maximal two-colored components in each step. Vigoda's result was the best known for general graphs for 20 years until Chen et al. (2019) established optimal mixing of the flip dynamics for $k>(11/6-\varepsilon)Δ$ where $\varepsilon\approx 10^{-5}$. We present the first substantial improvement over these results. We prove an optimal mixing-time bound of $O(n\log{n})$ for the flip dynamics when $Δ\geq125$ and $k\geq1.809Δ$. This yields, through recent spectral independence results, an optimal $O(n\log{n})$ mixing time for the Glauber dynamics for every fixed $Δ\geq125$ in the same range of $k/Δ$. Our proof utilizes path coupling with a simple weighted Hamming distance for "unblocked" neighbors.

cs.DM↗