In this section, we will discuss the population of connected wireless sensor and/or actor networks, and how to generate one particular sample from the population for the purpose of simulating them and evaluating performance of proposed communication protocols. Typically, in literature, connected *random UDG* is employed in generating wireless sensor and/or actuator networks. It is generated by placing a group of nodes in a specific area pattern, such as a rectangle or a circle. The positions of *N* nodes are randomly determined (e.g., by selecting their two or three coordinates at random) and are independent from each other. The desired network topology is achieved once the generated topology passes the connectivity test (usually by running centralized Dijkstra's shortest path algorithm). The expected node *degree* (average number of neighbors per node) is the number of remaining nodes, *N − 1*, times the probability that any node will be placed within the node's transmission area. This probability can be approximately calculated by dividing the transmission area by the total area. Thus the expected degree, *d* is ≈ (*N* − 1) × *πr*^{2}/*A*, where *A* is the area of the region of interest and *r* is the transmission radius. That is, . The exact average degree *D* for the generated graph is only an approximation of the desirable average degree ...

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