# Get Ad-hoc Networks: Fundamental Properties and Network PDF

By Ramin Hekmat

ISBN-10: 1402051654

ISBN-13: 9781402051654

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Extra resources for Ad-hoc Networks: Fundamental Properties and Network Topologies

Example text

3) where rij is the normalized distance between two placeholders i and j in the service area of the ad-hoc network. The service area of the ad-hoc network is the whole area where nodes are uniformly distributed. 3) for diﬀerent sizes of square-shaped service areas and for diﬀerent values of ξ. Important is to notice that when the size of the service area increases, the link density tends to zero. Further, we see that the link density is higher for larger values of ξ. From a radio propagation point of view, a higher value of ξ means more signal power ﬂuctuations that results into higher probability of having occasional links with nodes at farther distances.

This result has been proved in both [50] and [44]. 2 Regular lattice graph model A regular lattice graph is constructed with nodes (vertices) placed on a regular grid structure. Adjacent nodes on the grid are all equidistant (although this distance can be deﬁned to be non-metric). The probability that two adjacent nodes on the grid are connected is p. Non-adjacent nodes cannot be linked directly. Links (edges) are then created independently and are all equiprobable. 5 shows an example of a 2-dimensional lattice graph on a square grid of size 10 × 20 for two diﬀerent values of p.

Unless stated otherwise, the term ”random graph” in this book will refer to the Erd¨ os and R´enyi random graph. A random graph with N vertices and L edges can be constructed by starting with N vertices and zero edges. 1 Erd¨ os and R´enyi random graph model 19 and independently from the N (N − 1)/2 possible edges. In total, there are N (N −1)/2 equiprobable random graphs with N vertices and L edges. AnL other way of looking at random graphs is the assumption that any pair of vertices in a random graph is connected with the probability p.