The clustering activity is an unsupervised learning observation which coalesces the data into segments. Grouping of data is done by identification of common characteristics that are labeled as similarities among data on the basis of their characteristics. Graph clustering is a tool needed in many computer applications, such as network routing, analysis of social networks, computer vision, and VLSI physical design. This chapter explains how quantum random walk helps in graph-based clustering, and we propose a new quantum clustering algorithm. The proposed quantum clustering algorithm is based on the discrete-time quantum random walk, which finds the clusters from a given adjacency matrix of a graph. We give a quantum circuit model and Quantum Computing Language-based simulation of our algorithm and illustrate its faster rate of convergence. Simulation results for experimental graphs illustrate that our proposed algorithm shows an exponential speedup over existing classical algorithms. © 2017 Elsevier Inc. All rights reserved.