Network theory leads to a new way to investigate the dynamics of complex systems. As a result, many methods were proposed to construct a network from nonlinear time series. However, most previous works focused on deriving the adjacency matrix to represent the complex network and extract network-theoretic measures. Although the adjacency matrix provides connectivity information of nodes and edges, the network geometry can take variable forms. The definite network topology remains unknown. This paper develops a self-organizing approach to derive the steady geometric structure of a network from the adjacency matrix. As such, novel network-theoretic measures can be achieved based on actual node-to-node distances in the self-organized network topology.