  The closed-form solution for the average distance of a deterministic
network--Sierpinski network--is found. This important quantity is calculated
exactly with the help of recursion relations, which are based on the
self-similar network structure and enable one to derive the precise formula
analytically. The obtained rigorous solution confirms our previous numerical
result, which shows that the average distance grows logarithmically with the
number of network nodes. The result is at variance with that derived from
random networks.
