Algebraic connectivity

Algebraic Connectivity

Algebraic connectivity

to get instant updates about 'Algebraic Connectivity' on your MyPage. Meet other similar minded people. Its Free!

X 

All Updates


Description:
The algebraic connectivity of a graph G is the second-smallest eigenvalue of the Laplacian matrix of G. This eigenvalue is greater than 0 if and only if G is a connected graph. This is a corollary to the fact that the number of times 0 appears as an eigenvalue in the Laplacian is the number of connected components in the graph. The magnitude of this value reflects how well connected the overall graph is, and has been used in analysing the synchronizability of networks.

Properties

The algebraic connectivity of a graph G is greater than 0 if and only if G is a connected graph. Furthermore, the value of the algebraic connectivity is bounded above by the traditional (vertex) connectivity of the graph.J.L. Gross and J. Yellen. Handbook of Graph Theory, CRC Press, 2004, page 314. If the number of vertices of a connected graph is n and the diameter is D, the algebraic connectivity is known to be bounded below by 1/nD,J.L. Gross and J. Yellen. Handbook of Graph Theory, CRC Press, 2004, page 571. and in fact (in a result due to Brendan McKay) by 4/nD.Bojan Mohar, , in Graph Theory, Combinatorics, and Applications, Vol. 2, Ed. Y. Alavi, G. Chartrand, O. R. Oellermann, A. J. Schwenk, Wiley, 1991, pp. 871–898. For the example shown above, for example,...
Read More

No feeds found

All
Posting your question. Please wait!...


No updates available.
No messages found
Suggested Pages
Tell your friends >
about this page
 Create a new Page
for companies, colleges, celebrities or anything you like.Get updates on MyPage.
Create a new Page
 Find your friends
  Find friends on MyPage from