Parallel data processing is one of the specific infrastructure applications categorized as a service provided by cloud computing. In cloud computing environments, data-intensive applications increasingly use the parallel processing paradigm known as MapReduce. MapReduce is based on a strategy called "divide and conquer," which uses ordinary computers, also called "nodes," to do processing in parallel. This paper looks at how open multiprocessing (OpenMP), the best shared-memory parallel programming model for high-performance computing, can be used in the MapReduce application using proposed fractal network models. Two fractal network models are offered, and their work is compared with a well-known network model, the hypercube. The first fractal network model achieved an average speedup of 3.239 times while an efficiency ranged from 73-95%. In the second model of the network, the speedup got to 3.236 times while keeping an efficiency of 70-92%. Furthermore, the path-finding algorithm employed in the recommended fractal network models remarkably identified all paths and calculated the shortest and longest routes.