This paper analyzes how agents' perception of relationships with others determines the structures of networks. In our model, agents are endowed with their own multi-dimensional characteristics and form links depending on the social
distance between them. We characterize average path length and clustering coefficient in stable networks, and analyze how they are related to the way social distances are measured by agents. One implication is that the introduction of new
communication technology makes a network closely connected but not cliquish. We relate our model and results to Granovetter's ``strength of weak ties hypothesis," Tversky's ``similarity scale," and Mobius-Rosenblat's ``communication externality."