An Energy-Efficient Clustering Routing Algorithm Based on Geographic Position and Residual Energy for Wireless Sensor Network

Algorithm 1

Clustering step.

Given a set of sensor nodes

that we want to cluster into clusters.

(1) Form the affinity matrix defined by:

(2) Define to be the diagonal matrix whose ()—

is the sum of A’s th row, and construct the matrix

(3) Find the largest eigenvector of (chosen

to be orthogonal to each other in the case of repeated

eigenvalues) and form the matrix

by stacking the eigenvectors in columns.

(4) Treating each row of as a point in , cluster them

into clusters via -means.

(5) Finally, assign the sensor node to cluster if and

only if row of the matrix was assigned to cluster .