Subject: [manet] A graph growth problem

From: Yujie Zhu <[email-masked]>
Date: Fri, 19 Nov 2004 11:51:07 -0500

Hi all:

I'm looking into a graph growth problem described as follows:
Consider a large scale sensor network with nodes uniformly
distributed in a finite field. A shortest path tree is generated
from sink located at the center of the field to all other sensor
nodes. Is there any analytical formula
that characterizes the number of nodes at j hops from the sink
on the shortest path tree(defined as Q(j))? For infinite random graph and
k-ary trees,  Q(j) increases exponentially, but I'm not sure
if this is true for finite networks with uniform node distribution.
 From a simple simulation it seems that
Q(j) increases in a superlinear fashion within a certain
hops, then decrease dramatically.
Does anybody aware of any existing solution to this problem?

Thanks in advance,

Yujie Zhu

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