  In this paper, we investigate stable matching in structured networks.
Consider case of matching in social networks where candidates are not fully
connected. A candidate on one side of the market gets acquaintance with which
one on the heterogeneous side depends on the structured network. We explore
four well-used structures of networks and define the social circle by the
distance between each candidate. When matching within social circle, we have
equilibrium distinguishes from each other since each social network's topology
differs. Equilibrium changes with the change on topology of each network and it
always converges to the same stable outcome as complete information algorithm
if there is no block to reach anyone in agent's social circle.
