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Consider a graph with N nodes. All nodes are distributed as a Poisson point process with density of λ in a L*L area. There is an edge between two nodes if and only if the distance between them is less than or equal to R. What is the adjacency matrix of this graph? What is the distribution of 0,1 in this adjacency matrix?

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closed as off-topic by Bill Johnson, Andrey Rekalo, Theo Johnson-Freyd, Noah Stein, Ryan Budney Jul 25 '13 at 21:16

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Bill Johnson, Andrey Rekalo, Noah Stein, Ryan Budney
If this question can be reworded to fit the rules in the help center, please edit the question.

The correct terminology is "adjacency matrix" – Yemon Choi Jul 25 '13 at 5:18

Seems like you need to read up on "What is a random geometric graph?" before posing further similar questions on this site. There are many references; for mathematics I would suggest:

Matthew Penrose Random Geometric Graphs Oxford University Press (2003)

Mark Walters Random Geometric Graphs in Surveys in Combinatorics London Mathematical Society (2011).

For applications in wireless networks:

Guoqiang Mao and Brian D. O. Anderson, IEEE/ACM Trans. Network. 20 408-421 (2012).

Justin P. Coon, Carl P. Dettmann and Orestis Georgiou, J. Stat. Phys. 147 758-778 (2012).

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