Science Fair Projects Ideas - Admittance matrix

All Science Fair Projects

 		      

Science Fair Project Encyclopedia for Schools!
  Search    Browse    Forum  Coach    Links    Editor    Help    Tell-a-Friend    Encyclopedia    Dictionary     

Science Fair Project Encyclopedia

For information on any area of science that interests you,
enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
Or else, you can start by choosing any of the categories below.

Science Fair Project Encyclopedia Contents Page

Admittance matrix

In the mathematical field of graph theory the admittance matrix or Laplacian matrix is a matrix representation of a graph. Together with Kirchhoff's theorem it can be used to calculate the number of spanning trees for a given graph.

Definition

The admittance matrix of a graph G is defined as

L: = D - A

with D the degree matrix of G and A the adjacency matrix of G.

More explicitly, given a graph G with n vertices the admittance matrix L:=(l_{i,j})_{n \times n} is defined as

l_{i,j}:=\left\{ \begin{matrix} \deg(v_i) & \mbox{if}\ i = j \\ -1 & \mbox{if}\ i \neq j\ \mbox{and}\ v_i\ \mbox{adjacent}\ v_j \\ 0 & \mbox{otherwise} \end{matrix} \right.

In the case of directed graphs, either the indegree or the outdegree might be used, depending on the application.

See also

Science Fair Project Encyclopedia Contents Page
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
Science kits, science lessons, science toys, maths toys, hobby kits, science games and books - these are some of many products that can help give your kid an edge in their science fair projects, and develop a tremendous interest in the study of science. When shopping for a science kit or other supplies, make sure that you carefully review the features and quality of the products. Compare prices by going to several online stores. Read product reviews online or refer to magazines.

Start by looking for your science kit review or science toy review. Compare prices but remember, Price $ is not everything. Quality does matter.
Science Fair Coach
What do science fair judges look out for?
ScienceHound
Science Fair Projects for students of all ages
All Science Fair Projects.com Site
All Science Fair Projects Homepage
Search | Browse | Links | From-our-Editor | Books | Help | Contact | Privacy | Disclaimer | Copyright Notice