This paper describes a number of characteristics in ad hoc network with a dynamic topology, like the neighbour nodes, the area of the ad hoc network, number of nodes, node density, and area of transmission. The theoretical analysis of their effectives are discussed and proved that the topology of a network has a clear effect under changing these characteristics. Moreover, we show the effects of the number of nodes and neighbour node on the mobility. Furthermore, we characterize the Critical Transmitting Range (CTR) for connectivity in case of random waypoint (RWP) mobility. Many theoretical experiments are performed on the properties of the nodes such as: the links between nodes to routes in the network, the effected of nodes on traffic rate, probability of node failure, and the mobility of the network to ensure that the connectivity of the network is still connected with high node density. Keywords: ad hoc networks, routing protocols, network density, probability of the node failure, traffic affected and mobility.