Recently hashing with multiple tables has become attractive in many real life applications, owing to its theoretical guarantee and practical success. To pursue the desired performance, usually great efforts are required on the hashing algorithm design for the specified scenario. Hash bit selection serves as a general method that can provide satisfying performance for different scenarios by utilizing existing hashing algorithms. In this paper, a novel bit selection framework via walks on graph is proposed to support both compact hash code generation and complementary hash table construction. It formulates the selection problem as the subgraphs discovery on an edge- and vertex-weighted graph, where the most desired subset corresponds to the frequently visited ones (bits/tables) in a Markov process. The framework is unified and compatible with different hashing algorithms. For compact code generation, it selects the most independent and informative hash bits using the Markov process over the candidate bit graph. For complementary hash table construction, it exploits the hierarchical authority relations among all candidate bits and separates them into a number of bit subsets as the candidate tables, from which multiple complementary hash tables can be efficiently selected. Experiments are conducted for two important selection scenarios, i.e., hashing using different hashing algorithms and hashing with multiple features. The results indicate that our proposed selection framework achieves significant performance gains over the naive selection methods under different scenarios. (C) 2016 Elsevier B.V. All rights reserved.