Recent studies have shown that various models can explain the emergence of complex networks, such as scale-free and small-world networks. This paper presents a different model to generate complex networks using a multi-agent approach. Each node is considered as an agent. Based on voting by all agents, edges are added repeatedly. We use four different kinds of centrality measures as a utility functions for agents. Depending on the centrality measure, the resultant networks differ considerably: typically, closeness centrality generates a scale-free network, degree centrality produces a random graph, betweenness centrality favors a regular graph, and eigenvector centrality brings a complete subgraph. The importance of the network structure among agents is widely noted in the multi-agent research literature. This paper contributes new insights into the connection between agents' local behavior and the global property of the network structure. We describe a detailed analysis on why these structures emerge, and present a discussion of the possible expansion and application of the model.