Exploring small world effect in ad hoc network

Abstract

Small world is a highly clustered i.e., a densely and fully connected network, with low degree of separation between the nodes. These networks have inherited the high clustering property of regular networks and low average path length property of random network, thus giving an efficient network compared to both. The parameters used to quantify the above mentioned properties are clustering coefficient C and characteristic path length L respectively. Small world property was noticed in many real world networks and many people tried to convert the existing networks into small world networks. Similar model is used in this thesis, which adds a single node with a long radio range in n × n square grid network along with other nodes having small and same radio range. Considering this network model, we have worked to come up with mathematical equations of the parameters L,C and efficiency e of network before and after adding the long radio range node in a square grid network.