  We present a mathematical description of the voter model dynamics on
heterogeneous networks. When the average degree of the graph is $\mu \leq 2$
the system reaches complete order exponentially fast. For $\mu >2$, a finite
system falls, before it fully orders, in a quasistationary state in which the
average density of active links (links between opposite-state nodes) in
surviving runs is constant and equal to $\frac{(\mu-2)}{3(\mu-1)}$, while an
infinite large system stays ad infinitum in a partially ordered stationary
active state. The mean life time of the quasistationary state is proportional
to the mean time to reach the fully ordered state $T$, which scales as $T \sim
\frac{(\mu-1) \mu^2 N}{(\mu-2) \mu_2}$, where $N$ is the number of nodes of the
network, and $\mu_2$ is the second moment of the degree distribution. We find
good agreement between these analytical results and numerical simulations on
random networks with various degree distributions.
