
Contents
1 Introduction
Get access-
Published:March 1998
Cite
Abstract
A graph is a useful abstraction of many real world situations. It occurs when a problem is essentially related to the structure of interconnections between some objects. For example, a road map can be viewed as a graph: the interconnected objects are cities and connections correspond to roads. The connections can be one-way or two-way, and the corresponding graph can be directed or undirected. Another real world example is a group of people, the connections between them corresponding to the relation “the person x knows the person y”. In abstract graph terminology the interconnected objects (cities, persons) are called vertices or nodes (these terms are equivalent terms in this book). The connections are called edges. In the case of relation “x knows y” we have an edge ( x, y). A graph G is formally given by a pair G = (V, E), where V is the set of vertices and E is the set of edges. The edges can be unordered pairs of different vertices: the graph is called undirected; or ordered pairs: the graph is directed. We consider only the case when all edges are undirected or all edges are directed. Also we do not allow multiple edges between the same vertices (in the directed case between the same ordered pair). We assume that V is finite and its cardinality is usually denoted by n. This is the main parameter related to the size of the graph. The second parameter is the number m of edges of a given graph.
Sign in
Personal account
- Sign in with email/username & password
- Get email alerts
- Save searches
- Purchase content
- Activate your purchase/trial code
- Add your ORCID iD
Purchase
Our books are available by subscription or purchase to libraries and institutions.
Purchasing informationMonth: | Total Views: |
---|---|
September 2024 | 2 |
Get help with access
Institutional access
Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:
IP based access
Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.
Sign in through your institution
Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.
If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.
Sign in with a library card
Enter your library card number to sign in. If you cannot sign in, please contact your librarian.
Society Members
Society member access to a journal is achieved in one of the following ways:
Sign in through society site
Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:
If you do not have a society account or have forgotten your username or password, please contact your society.
Sign in using a personal account
Some societies use Oxford Academic personal accounts to provide access to their members. See below.
Personal account
A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.
Some societies use Oxford Academic personal accounts to provide access to their members.
Viewing your signed in accounts
Click the account icon in the top right to:
Signed in but can't access content
Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.
Institutional account management
For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.