Skip to main content Accessibility help

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.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

3 results

  • 2 - Local Convergence of Random Graphs

  • from Part I - Preliminaries
  • Remco van der Hofstad, Technische Universiteit Eindhoven, The Netherlands
  • Book:
    Random Graphs and Complex Networks
    Published online:
    08 February 2024
    Print publication:
    08 February 2024, pp 48-94

  • Summary

    In this chapter we discuss local convergence, which describes the intuitive notion that a finite graph, seen from the perspective of a typical vertex, looks like a certain limiting graph. Local convergence plays a profound role in random graph theory. We give general definitions of local convergence in several probabilistic senses. We then show that local convergence in its various forms is equivalent to the appropriate convergence of subgraph counts. We continue by discussing several implications of local convergence, concerning local neighborhoods, clustering, assortativity, and PageRank. We further investigate the relation between local convergence and the size of the giant, making the statement that the giant is “almost local” precise.

  • 3 - Norms and Normed Spaces

  • from Part II - Normed Linear Spaces
  • James C. Robinson, University of Warwick
  • Book:
    An Introduction to Functional Analysis
    Published online:
    21 March 2020
    Print publication:
    12 March 2020, pp 35-52

  • Summary

    We define the notion of a norm and a normed space. We prove that various canonical definitions are indeed norms (e.g. the l^p norm, the L^p norm, and the supremum norm). We discuss convergence, equivalent norms, and various notions of isomorphism between normed spaces. Finally, we discuss separability in more detail.

  • ON ISOMORPHISMS OF VERTEX-TRANSITIVE CUBIC GRAPHS

  • Part of
  • JING CHEN, CAI HENG LI, WEI JUN LIU
  • Journal:
    Journal of the Australian Mathematical Society / Volume 99 / Issue 3 / December 2015
    Published online by Cambridge University Press:
    13 August 2015, pp. 341-349
    Print publication:
    December 2015
    • Article
      • You have access
    • PDF
    • Export citation

  • We study the isomorphism problem of vertex-transitive cubic graphs which have a transitive simple group of automorphisms.