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Small-world network concept deals with the addition of a few Long-ranged Links (LLs) to significantly bring down the average path length (APL) of the network. The existing small-world models do not consider the real constraints of wireless networks such as the transmission range of LLs, limited radios per mesh router, and limited bandwidth for wireless links, therefore, we propose C-SWAWN (Constrained Small-World Architecture for Wireless Network) model for Wireless Mesh Networks (WMNs). We then propose three LL addition strategies for reducing APL to the centrally placed Gateway node in WMNs. In moderately large WMNs, a 43% reduction in APL to Gateway can be achieved with the addition of 10% LLs (with respect to number of mesh routers) in our C-SWAWN model with greedy LL addition strategy. Detailed studies show realistic performance benefits with application of small-world concept in WMNs.