  We consider the phenomenon of Bose-Einstein condensation in a random growing
directed network. The network grows by the addition of vertices and edges. At
each time step the network gains a vertex with probabilty $p$ and an edge with
probability $1-p$. The new vertex has a fitness $(a,b)$ with probability
$f(a,b)$. A vertex with fitness $(a,b)$, in-degree $i$ and out-degree $j$ gains
a new incoming edge with rate $a(i+1)$ and an outgoing edge with rate $b(j+1)$.
The Bose-Einstein condensation occurs as a function of fitness distribution
$f(a,b)$.
