  The prevalence of wealth inequality propels us to characterize its origin and
progression, via empirical and theoretical studies. The Yard-Sale(YS) model, in
which a portion of the smaller wealth is transferred between two individuals,
culminates in the concentration of almost all wealth to a single individual,
while distributing rest of the wealth with a power-law of exponent one. By
incorporating redistribution to the model, in which the transferred wealth is
proportional to the sender's wealth, we show that such extreme inequality is
suppressed if the frequency ratio of redistribution to the YS-type exchange
exceeds the inverse of the population size. Studying our model on a
sparsely-connected population, we find that the wealth inequality ceases to
grow for a period, when local rich nodes can no longer acquire wealth from
their broke nearest neighbors. Subsequently, inequality resumes growth due to
the redistribution effect by allowing locally amassed wealth to move and
coalesce. Analyzing the Langevin equations and the coalescing random walk on
complex networks, we elucidate the scaling behaviors of wealth inequality in
those multiple phases. These findings reveal the influence of network structure
on wealth distribution, offering a novel perspective on wealth inequality.
