I need to generate a random wireless network of nodes over an area 1000 x 1000 m2 having a specified average number of neighbors along the nodes. So, is there an equation or a certain random distribution that relates average no. of neighbors with total number of nodes in the network and direct coverage distance which is also given?
Random networks or graphs is a well studied subject, and with the Internet it gained more interest (though many other areas need random structures).
See review in http://mathinsight.org/generating_networks_desired_degree_distribution
The model you are asking is a bit specific so it needs deeper investigation to see what the model is exactly (especially the embedding in a square area), so it requires deeper understanding (beyond what an answer can give).
For some specific cases which may help you are in here:
(1) In power grid generation, see: http://santafe.edu/media/cms_page_media/702/Power%20Grid%20Project%20-%20Part%20I%20-%20vf.pdf
(2) In biological systems, see: http://www.tau.ac.il/lifesci/departments/zoology/members/stone/documents/Generatinguniformlydistributedrandomnetworks.pdf
Deployed invisible Nodes scavengers (unwired links) to seek out flirting partners(Θ(log n)1 (+) increase (8)+ or (deploy asymptotical network connection with probability (index) n increases (digital)
I think this is done by using A pseudorandom number generator (PRNG) : it is a deterministic algorithm which given a truly random binary sequence of length k, outputs a binary sequence of length l >> k with “appears” to be random.
The input to the PRNG is called the seed, while the output generator is called a pseudorandom bit sequence. Additionally, it used for cryptographic applications, the generator must not be subject to observation or manipulation by an adversary. Random numbers generators based on natural sources of randomness are subject to influence by external factors, and also to malfunction
If I correctly understood the question, one possibility is the following.
From the wireless range r (disc model, I suppose) and the average number of neighbors n, you calculate the node density d = n / ( r^2 x pi). Then, you divide your region into a grid of small squares of area A (the smaller, the better). In each small region you place a node with probability p = d x A.
If A is small enough, you are placing with good approximation the nodes randomly in your region, with density d. The nodes will have the required average number of neighbors n.
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