Measuring the connectivity of a cognitive radio ad-hoc network

In Cognitive Radio Ad-Hoc Networks (CRAHN) the behavior of the primary users influences the secondary network connectivity and the relevant performance. The methodologies used to evaluate network connectivity have to be worked up to take into account this aspect. In this letter we propose the use of Laplacian matrix and its second smallest eigenvalue to measure the network algebraic connectivity of a CRAHN. We re-elaborate the Laplacian matrix in order to have in its second smallest eigenvalue a function of the primary users behavior expressed as an activity factor. In this way we are able to monitor the algebraic connectivity of CRAHNs. This metric can be a useful instrument for network planning, data routing and network maintenance. Performance results show how this methodology can be efficiently applied in this kind of networks.