A self-organization of efficient and robust networks is important for a future design of communication or transportation systems, however both characteristics are incompatible in many real networks. Recently, it has been found that the robustness of onion-like structure with positive degree-degree correlations is optimal against intentional attacks. We show that, by biologically inspired copying, an onion-like network emerges in the incremental growth with functions of proxy access and reinforced connectivity on a space. The proposed network consists of the backbone of tree-like structure by copyings and the periphery by adding shortcut links between low degree nodes to enhance the connectivity. It has the fine properties of the statistically selfaveraging unlike the conventional duplication-divergence model, exponential-like degree distribution without overloaded hubs, strong robustness against both malicious attacks and random failures, and the efficiency with short paths counted by the number of hops as mediators and by the Euclidean distances. The adaptivity to heal over and to recover the performance of networking is also discussed for a change of environment in such disasters or battlefields on a geographical map. These properties will be useful for a resilient and scalable infrastructure of network systems even in emergent situations or poor environments.In this paper, we consider a self-organized design of efficient and robust networks by biologically inspired copying. In particular, we focus on the robust network structure Model Mechanism Reference network preferential [2] attachment cultural change, copying or [3], [4], [5] network duplication [6], [7] trail, survival [8] network [9], [10] cracking, fragmentation or [11], [12] network subdivision [13], [14], [15], [16] cluster of mass, aggregation [12] network [17] TABLE I. TYPICAL SELF-ORGANIZATION MECHANISMS. with positive degree-degree correlations [29], [30], [31]and an incrementally growing mechanism. The self-propagation in maintaining the robust structure is particularly important for the scalability of network system without degrading the performance.The organization of this paper is as follows. In Sec. II, we briefly review related network models to ours. In Sec. III, we propose a basic model for understanding the fundamental mechanism of network self-organization from a viewpoint in complex network science [18], [19], [20], [21] which aims to elucidate the universal properties and the generation rule of networks. We show the important properties of our model for the robustness of connectivity and the emergent functions. In Sec. IV, we consider an incrementally growing mechanism, and investigate the strong robustness and the efficiency for path lengths. We emphasis that the performance of our proposed networks for both the robustness and the efficiency does not degrade rather rises through the growth. In Sec. V, we discuss the possibilities and the issues for applications especially in communication or transportation systems. The adaptivity fo...