  In this work, a novel model of the random geometric graph (RGG), namely the
isotropic random geometric graph (IRGG) has been developed and its topological
properties in two dimensions have been studied in details. The defining
characteristics of RGG and IRGG are the same --- two nodes are connected by an
edge if their distance is less than a fixed value, called the connection
radius. However, IRGGs have two major differences from regular RGGs. Firstly,
the shape of their boundaries --- which is circular. It brings very little
changes in final results but gives a significant advantage in analytical
calculations of the network properties. Secondly, it opens up the possibility
of an empty concentric region inside the network. The empty region contains no
nodes but allows the communicating edges between the nodes to pass through it.
This second difference causes significant alterations in physically relevant
network properties such as average degree, connectivity, clustering coefficient
and average shortest path. Analytical expressions for most of these features
have been provided. These results agree well with those obtained from
simulations. Apart from the applicability of the model due to its symmetry and
simplicity, the scope of incorporating a penetrable cavity makes it suitable
for potential applications in wireless communication networks that often have a
node-free region.
