An emergent method for self-organizing a new small-world (SW) network with less average path-length than those of conventional small-world networks is proposed. The method is inspired by Ant- Colony Optimization (ACO), which is based on a pheromone trail formation by a collective behavior of ants. The resultant network architecture includes some "star" structure nodes with many degrees and other peripheral nodes with a few degrees. We called it a multi-star network, and analyzed its corresponding property of an n-star network theoretically and experimentally, comparing with typical conventional complex networks such as a random graph, WS (Watts-Stragatz) model and BA (Barabasi-Albert) model. We found that the new small-world network has an interesting property compared to other conventional complex networks, and it seems to reflect a real-world phenomenon such as the behavior of some "star" persons and their followers in a Twitter community and/or a Social Networking Service (SNS).