The k nearest neighbor (kNN) query is an essential graph data-management tool used for finding relevant data entities suited to a user-specified query node. Graph indexing methods have the potential to achieve a quick kNN search response and thus are promising approaches. However, they struggle to handle large-scale attributed complex networks. This is because constructing indices and querying kNN nodes in large-scale networks are computationally expensive, and they are not designed to handle node attributes included in the networks. In this paper, we propose a novel graph indexing algorithm, namely CT index, for fast kNN queries on large complex networks. To overcome the aforementioned limitations, our algorithm generates two types of indices based on the topological properties of complex networks. In addition, we further propose BAG index along with CT index so that our algorithm enables to explore kNN nodes based on the attribute similarity. Our extensive experiments on real-world graphs show that our algorithm achieves up to 18,074 times faster indexing and 146 times faster kNN query than other state-of-the-art methods.