Zipf's law is one of the best-known empirical regularities of the city-size distribution. There is extensive research on the subject, where each city is treated symmetrically in terms of the cost of transactions with other cities. Recent developments in network theory facilitate the examination of an asymmetric transport network. Under the scale-free transport network framework, the chance of observing extremes becomes higher than the Gaussian distribution predicts and therefore it explains the emergence of large clusters. City-size distributions share the same pattern. This paper proposes a way to incorporate network structure into urban economic models and explains the city-size distribution as a result of transport cost between cities.