Neural architecture search enables automation of architecture design. Despite its success, it is computationally costly and does not provide an insight on how to design a desirable architecture. Here we propose a new way of searching neural network where we search neural architecture by rewiring the corresponding graph and predict the architecture performance by graph properties. Because we do not perform machine learning over the entire graph space and use predicted architecture performance to search architecture, the searching process is remarkably efficient. We find graph based search can give a reasonably good prediction of desirable architecture. In addition, we find graph properties that are effective to predict architecture performance. Our work proposes a new way of searching neural architecture and provides insights on neural architecture design.