The big data term identifies datasets according to size and complexity. The traditional techniques such as data mining methods cannot manipulate big data. Extracting useful knowledge or hidden patterns from these massive datasets based on velocity, variety, volume, veracity, and value is called big data analytics. Graph databases are increased everywhere. Structural relationships between objects build a graph model. There are many applications for graph models such as social networking, biology, chemistry, image segmentation, web-link analysis, computer networks, and human genome assembly. The graph mining process deals with graph data by utilizing the methods of machine learning and data mining. The primary goal of graph mining is detecting useful and unexpected patterns. Big graph mining processes extract significant information from massive graph data. In this thesis, a parallel local clustering algorithm is proposed for improving the quality of the cluster. This algorithm solves problems in community detection, image segmentation, etc. The proposed algorithm modifies the local flow-based method to reach the best runtime as well as realizing the flexibility and ease of implementation. Clustering large graphs detect good conductance of the clusters. SimpleLocal is introduced and analyzed for locally-biased graph-based learning. It finds good conductance cuts near a set of seed vertices but consumes more time. In this thesis, a new Parallel SimpleLocal (PSL) system is proposed for shared memory parallel architectures (e.g., multi-core CPUs). The computation time problem is addressed in existing related methods by using parallel solutions. This technique is applied to important applications such as image segmentation and community detection for accelerating the process. Multi-core CPUs are a robust processing parallel architecture.