This article presents a comparison of the computing performance of the MapReduce tool Hadoop and Giraph on large-scale graphs. The main ideas of MapReduce and bulk synchronous parallel (BSP) are reviewed as big data computing approaches to highlight their applicability in large-scale graph processing. This paper reviews the execution performance of Hadoop and Giraph on the PageRank algorithm to classify web pages according to their relevance, and on a few other algorithms to find the minimum spanning tree in a graph with the primary goal of finding the most efficient computing approach to work on large-scale graphs. Experimental results show that the use of Giraph for processing large-size graphs reduces the execution time by 25% in comparison with the results obtained using the Hadoop for the same experiments. Giraph represents the optimal option thanks to its in-memory computing approach that avoids secondary memory direct interaction.