### Abstract

A random graph process, G_{1}(n), is a sequence of graphs on n vertices which begins with the edgeless graph, and where at each step a single edge is added according to a uniform distribution on the missing edges. It is well known that in such a process a giant component (of linear size) typically emerges after (1+o(1))n=2 edges (a phenomenon known as "the double jump"), i.e., at time t = 1 when using a timescale of n/2 edges in each step.

Original language | English (US) |
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Pages (from-to) | 1853-1888 |

Number of pages | 36 |

Journal | Indiana University Mathematics Journal |

Volume | 59 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2010 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- Giant component
- Random graphs
- Wormald's differential equation method

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## Cite this

Amir, G., Gurel-Gurevich, O., Lubetzky, E., & Singer, A. (2010). Giant components in biased graph processes.

*Indiana University Mathematics Journal*,*59*(6), 1853-1888. https://doi.org/10.1512/iumj.2010.59.4008