  The construction of large-scale, low-latency networks becomes difficult as
the number of nodes increases. In general, the way to construct a theoretically
optimal solution is unknown. However, it is known that some methods can
construct suboptimal networks with low-latency. One such method is to construct
large-scale networks from optimal or suboptimal small networks, using the
product of graphs. There are two major advantages to this method. One is that
we can reuse small, already known networks to construct large-scale networks.
The other is that the networks obtained by this method have graph-theoretical
symmetry, which reduces the overhead of communication between nodes. A network
can be viewed as a graph, which is a mathematical term from combinatorics. The
design of low-latency networks can be treated as a mathematical problem of
finding small diameter graphs with a given number of nodes ( called order ) and
a given number of connections between each node ( called degree ). In this
paper, we overview how to construct large graphs from optimal or suboptimal
small graphs by using graph-theoretical products. We focus on the case of
diameter 2 in particular. As an example, we introduce a graph of order 256,
degree 22 and diameter 2, which granted us the Deepest Improvement Award at the
Graph Golf competition. Moreover, the average shortest path length of the graph
is the smallest in graphs of order 256 and degree 22.

Combinatorics