We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
from Part II - Erdős–Rényi–Gilbert Model
Published online by Cambridge University Press: 02 March 2023
In this chapter, we study some typical properties of the degree sequence of a random graph. We begin by discussing the typical degrees in a sparse random graph, i.e., one with cn/2 edges for some positive constant c. We prove some results on the asymptotic distribution of degrees. We continue by looking at the typical values of the minimum and maximum degrees in dense random graphs, i.e., when edge probability p is constant. Given these properties of the degree sequence of dense graphs, we can then describe a simple canonical labeling algorithm that enables one to solve the graph isomorphism problem on a dense random graph.
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.
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.
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.
