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Journal ArticleDOI

Plug-and-Play Network Reconfiguration Algorithms to Maintain Regularity and Low Network Reconfiguration Needs

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TLDR
Algorithms to connect and disconnect nodes to/from an existing graph are proposed, which are able to maintain the regularity of a graph while requiring minimal reconfiguration of the network.
Abstract
In this letter we propose algorithms to connect and disconnect nodes to/from an existing graph, which are able to maintain the regularity of a graph while requiring minimal reconfiguration of the network. Further, simulations suggest that the algorithms maintain a minimum bound on the algebraic connectivity of the graph. These properties of the algorithms suit their use in plug-and-play networks.

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References
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Book

Networks: An Introduction

Mark Newman
TL;DR: This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.
Journal ArticleDOI

Random graphs with arbitrary degree distributions and their applications.

TL;DR: It is demonstrated that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
Journal ArticleDOI

Are randomly grown graphs really random

TL;DR: It is concluded that grown graphs, however randomly they are constructed, are fundamentally different from their static random graph counterparts.
Proceedings ArticleDOI

Ultrafast consensus in small-world networks

TL;DR: It is demonstrated that it is possible to dramatically increase the algebraic connectivity of a regular complex network by 1000 times or more without adding new links or nodes to the network, implying that a consensus problem can be solved incredibly fast on certain small-world networks giving rise to a network design algorithm for ultra fast information networks.
Journal ArticleDOI

Generating Random Regular Graphs Quickly

TL;DR: A practical algorithm for generating random regular graphs for all d growing as a small power of n, in the sense that all d-regular graphs on n vertices have in the limit the same probability as n → ∞.