A random graph generation algorithm for the analysis of social networks

Morris, James F.; O'Neal, Jerome W.; Deckro, Richard F.

doi:10.1177/1548512912450370

Cited by 6 publications

(2 citation statements)

References 25 publications

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“…While simulation of computer networks has always played an important role in the design and development of networks as well as protocols and algorithms 9 , due to the above-mentioned increase in the scale and order of complexity, there is a need for newer and more effective techniques and paradigms for modeling and simulation of large-scale networks. As a follow-up to the first part of the special issue on Complex Adaptive COmmunicatiOn Networks and environmentS (CACOONS) 10 , this second part presents a selection of four peer-reviewed papers on the use of two complexity-related multidisciplinary modeling and simulation techniques, namely, agent-based modeling (ABM) 11 and complex networks–based modeling (CN) 12 .…”

Section: Complexity In Communication Networkmentioning

confidence: 99%

“…As a follow-up to the first part of the special issue on Complex Adaptive COmmunicatiOn Networks and environmentS (CACOONS) 10 , this second part presents a selection of four peer-reviewed papers on the use of two complexity-related multidisciplinary modeling and simulation techniques, namely, agent-based modeling (ABM) 11 and complex networks-based modeling (CN) 12 .…”

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confidence: 99%

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Complex adaptive communication networks and environments: Part 2

Niazi

Hussain

2013

SIMULATION

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Section: Complexity In Communication Networkmentioning

confidence: 99%

mentioning

confidence: 99%

Complex adaptive communication networks and environments: Part 2

Niazi

Hussain

2013

SIMULATION

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Embedding theorems for random graphs with specified degrees

Gao,

Ohapkin

2024

Combinator. Probab. Comp.

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Given an $n\times n$ symmetric matrix $W\in [0,1]^{[n]\times [n]}$ , let ${\mathcal G}(n,W)$ be the random graph obtained by independently including each edge $jk\in \binom{[n]}{2}$ with probability $W_{jk}=W_{kj}$ . Given a degree sequence $\textbf{d}=(d_1,\ldots, d_n)$ , let ${\mathcal G}(n,\textbf{d})$ denote a uniformly random graph with degree sequence $\textbf{d}$ . We couple ${\mathcal G}(n,W)$ and ${\mathcal G}(n,\textbf{d})$ together so that asymptotically almost surely ${\mathcal G}(n,W)$ is a subgraph of ${\mathcal G}(n,\textbf{d})$ , where $W$ is some function of $\textbf{d}$ . Let $\Delta (\textbf{d})$ denote the maximum degree in $\textbf{d}$ . Our coupling result is optimal when $\Delta (\textbf{d})^2\ll \|\textbf{d}\|_1$ , that is, $W_{ij}$ is asymptotic to ${\mathbb P}(ij\in{\mathcal G}(n,\textbf{d}))$ for every $i,j\in [n]$ . We also have coupling results for $\textbf{d}$ that are not constrained by the condition $\Delta (\textbf{d})^2\ll \|\textbf{d}\|_1$ . For such $\textbf{d}$ our coupling result is still close to optimal, in the sense that $W_{ij}$ is asymptotic to ${\mathbb P}(ij\in{\mathcal G}(n,\textbf{d}))$ for most pairs $ij\in \binom{[n]}{2}$ .

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