Spatial growth network

I started with generating graph with nodes. And assigned points for
every nodes with in square drawn from (0,0) to (1,1). I took the vertex
0 and gave the fixed point (0.5,0.5) making it act like center.
I had two lists – disconnected_vertices and connected_vertices. I always
try to find an edge with lowest weight(calculated from given formula)
that connects disconnected_vertex to connected_vertex and add an edge.
The minimum weight function used is
wij=dij+∝((dij+lj0)/di0)
As alpha (∝) being factor of the ratio, increase of alpha makes all
vertices near to zero to connect to center vertex. Thus we see when
alpha  = 0, it is purely based on distance but when alpha increases we
see more vertices connected to center vertex as it considers the routing
time.
dij – the Euclidian distance formula , lj0 – shortest distance between j
and 0
This process is carried out until the graph becomes connected. It ends
up having (n-1) edges.