- Ad hoc, actuator and sensor wireless networks normally have critical connectivity properties before becoming fault intolerant. Existing algorithms for testing k-connectivity are centralized. In this article, we introduce localized algorithms for testing k-connectivity. In localized protocols, each node makes its own decision based on the information available in its local neighborhood. In the first proposed local neighbor detection (LND) algorithm, each node verifies whether or not itself and each of its p-hop neighbors have at least k neighbors. In the second local critical node detection (LCND) protocol, it also tests if the subgraph of its p-hop neighbours of a given node is k-connected. The third local subgraph connectivity detection (LSCD) protocol is based on communications between neighboring nodes to