Both Apache Graph and Tez are focused on Graph processing. Apache Giraph is a very popular tool for graph processing. A famous use-case for Giraph is the social graph at Facebook. Facebook uses Giraph to analyze how one might know a person in order to find out what other persons could be friends. Graph processing works on the travelling Sales-Person problem, trying to answer the question on what is the shortest way to get to the customers.
Apache Tez is focused on improving the performance when working with graphs. This makes the development ways easier and reduces the number of MapReduce jobs that are executed underneath it significantly. Apache Tez highly increases the performance against typical MapReduce queries and optimizes the resource management.
The following figure demonstrates graph processing with and without Tez.
MapReduce without Tez