Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-09T07:30:17.793Z Has data issue: false hasContentIssue false

6 - Random graphs and random mappings

Published online by Cambridge University Press:  18 March 2010

Get access

Summary

Introduction

This chapter is devoted to random graphs. A number of ways of introducing randomness for various classes of graph exists, one of which is to specify on some classes of graph (trees, forests, graphs of one-to-one mappings and so on) certain, as a rule uniform, probability distributions. The second way of constructing random graphs is defined by a stochastic process which gives a rule for joining a number of initially isolated vertices by edges. The third way, which is closely related to the second, is described by a random procedure of deletion of edges from a complete graph. Other methods for constructing random graphs exist but they are of little use.

Before proceeding to describe results in the field, we list a number of statements concerning the combinatorial properties of graphs that will be required in the sequel. In this chapter we deal mainly with labeled graphs and for this reason the results cited below are related, as a rule, to such combinatorial structures.

Trees

Labeled trees are, in a sense, the simplest labeled graphs. A tree is a connected graph with no cycles. A rooted tree is a tree which has a distinguished vertex called the root.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×