The evolution of random graphs
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This article is published in Transactions of the American Mathematical Society.The article was published on 1984-01-01 and is currently open access. It has received 5331 citations till now. The article focuses on the topics: Line graph & Voltage graph.read more
Citations
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Statistical mechanics of complex networks
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
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The Structure and Function of Complex Networks
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
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Consensus and Cooperation in Networked Multi-Agent Systems
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
Journal ArticleDOI
Complex brain networks: graph theoretical analysis of structural and functional systems
Edward T. Bullmore,Olaf Sporns +1 more
TL;DR: This article reviews studies investigating complex brain networks in diverse experimental modalities and provides an accessible introduction to the basic principles of graph theory and highlights the technical challenges and key questions to be addressed by future developments in this rapidly moving field.
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Error and attack tolerance of complex networks
TL;DR: It is found that scale-free networks, which include the World-Wide Web, the Internet, social networks and cells, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates.
References
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Journal ArticleDOI
On the structure of linear graphs
Paul Erdös,A. H. Stone +1 more
TL;DR: The first result in this direction was due to Turân as discussed by the authors, who proved that a graph with kn vertices and Ck, 2n+1 edges always contains a complete graph of order k + 1.
Book ChapterDOI
Graph Theory and Probability
TL;DR: A well-known theorem of Ramsay (8, 9) states that to every n there exists a smallest integer g(n) such that every graph of g n contains either a set of n independent points or a complete graph of order n.
Journal ArticleDOI
Calculus of Finite Differences
C. W. Jones,C. Jordan +1 more
TL;DR: On operations Functions important in the calculus of finite differences Inverse operation of differences and means, expansion of functions, interpolation, construction of tables Approximation and graduation Numerical solution of equations.