*S. N. Dorogovtsev and J. F. F. Mendes*

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198515906
- eISBN:
- 9780191705670
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515906.003.0007
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter describes the global organization of undirected and directed complex networks. This includes the statistics and structure of connected components in these networks, the emergence of a ...
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This chapter describes the global organization of undirected and directed complex networks. This includes the statistics and structure of connected components in these networks, the emergence of a giant connected component, and its relative size. The chapter discusses the resilience of complex networks against random breakdowns and failures and the spread of diseases within networks.Less

This chapter describes the global organization of undirected and directed complex networks. This includes the statistics and structure of connected components in these networks, the emergence of a giant connected component, and its relative size. The chapter discusses the resilience of complex networks against random breakdowns and failures and the spread of diseases within networks.

*Sergey N. Dorogovtsev*

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter gives insight into the simplest and most studied random networks: the classical random graphs. The Erdös–Rényi and Gilbert models are described, and some of their properties and ...
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This chapter gives insight into the simplest and most studied random networks: the classical random graphs. The Erdös–Rényi and Gilbert models are described, and some of their properties and characteristics are considered. These characteristics include a Poisson degree distribution, the number of loops and clustering, and average shortest-path length. The statistics of connected components in these random networks and the birth of a giant connected component, are considered.Less

This chapter gives insight into the simplest and most studied random networks: the classical random graphs. The Erdös–Rényi and Gilbert models are described, and some of their properties and characteristics are considered. These characteristics include a Poisson degree distribution, the number of loops and clustering, and average shortest-path length. The statistics of connected components in these random networks and the birth of a giant connected component, are considered.

*S. N. Dorogovtsev and J. F. F. Mendes*

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198515906
- eISBN:
- 9780191705670
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515906.003.0002
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter introduces the basic characteristics and notions of graph theory and the science of networks: degree, degree distribution, clustering coefficient, the average length of the shortest path ...
More

This chapter introduces the basic characteristics and notions of graph theory and the science of networks: degree, degree distribution, clustering coefficient, the average length of the shortest path between two nodes in a network, the size of a giant connected component, and others. The classical random graphs and their characteristics are introduced and explained. The contrasting types of degree distributions are discussed: namely, Poisson and scale-free distributions.Less

This chapter introduces the basic characteristics and notions of graph theory and the science of networks: degree, degree distribution, clustering coefficient, the average length of the shortest path between two nodes in a network, the size of a giant connected component, and others. The classical random graphs and their characteristics are introduced and explained. The contrasting types of degree distributions are discussed: namely, Poisson and scale-free distributions.