Transport infrastructure evolves over time in a complex process as part of a dynamic and open system including travel demand, land use, as well as economic and political initiatives. As transport infrastructure changes, each traveler may adopt a new schedule, frequency, destination, mode, and/or route, and in the long term may change the location of their activities. These new behaviors create demand for a new round of modifications of infrastructure. In the long run, we observe the collective change in the capacity, service, connectivity, and connection patterns (topology) of networks. This paper examines how a fixed set of places incrementally gets connected as transport networks are constructed and upgraded over time. A Simulator Of Network Incremental Connection (SONIC) is constructed to model the process of incremental connections and examines how networks evolve differently under centralized versus decentralized jurisdictional initiatives. Exploring the mechanism underlying this dynamic process can answer questions such as how urban networks have developed into various topologies, which network patterns are more efficient, and whether and how transport engineers, planners, and decision makers can guide the dynamics of land uses and infrastructure in a desired direction.