Another desirable property of interconnection networks is
* node symmetry*. A node symmetric network has no distinguished
node, that is, the ``view'' of the rest of the network is the same
from any node. Rings, fully connected networks, and hypercubes
are all node symmetric. Trees and stars, shown in
Figure 12,
are not. A tree has three different types of nodes, namely a root
node, interior nodes, and leaf nodes, each with a different
degree. A star has a distinguished node in the center which is
connected to every other node. When a topology is node asymmetric
a distinguished node can become a communications bottleneck.

A more formal definition of a communication bottleneck is based on
a property known as the * bisection width*, which is the minimum

Figure 12: Tree and Star.

number of links that must be cut in order to divide the topology
into two independent networks of the same size (plus or minus one
node). The bisection width of a tree is 1, since if either link
connected to the root is removed the tree is split into two
subtrees. The * bisection bandwidth* of a parallel system is the
communication bandwidth across the links that are cut in defining
the bisection width. This bandwidth is useful in defining worst-
case performance of algorithms on a particular network, since it
is related to the cost of moving data from one side of the system
to the other.