  We report on exact results for the degree $K$, the diameter $D$, the
clustering coefficient $C$, and the betweenness centrality $B$ of a
hierarchical network model with a replication factor $M$. Such quantities are
calculated exactly with the help of recursion relations. Using the results, we
show that (i) the degree distribution follows a power law $P_K \sim
K^{-\gamma}$ with $\gamma = 1+\ln M /\ln (M-1)$, (ii) the diameter grows
logarithmically as $D \sim \ln N$ with the number of nodes $N$, (iii) the
clustering coefficient of each node is inversely proportional to its degree, $C
\propto 1/K$, and the average clustering coefficient is nonzero in the infinite
$N$ limit, and (iv) the betweenness centrality distribution follows a power law
$P_B \sim B^{-2}$. We discuss a classification scheme of scale-free networks
into the universality class with the clustering property and the betweenness
centrality distribution.
