Modern Big Data increasingly appears in the form of complex graphs and networks. Examples include the physical Internet, the world wide web, online social networks, phone networks, and biological networks. In addition to their massive sizes, these graphs are dynamic, noisy, and sometimes transient. They also conform to all five Vs (Volume, Velocity, Variety, Value and Veracity) that define Big Data. However, many graph-related problems are computationally difficult, and thus big graph data brings unique challenges, as well as numerous opportunities for researchers, to solve various problems that are significant to our communities. Big graph problems are currently solved using several complementary paradigms. The most popular approach is perhaps by exploiting parallelism, through specialized algorithms for supercomputers, shared-memory multicore and manycore systems, and heterogeneous CPU-GPU systems. However, since real-world graphs are sparse and highly irregular, there are very few parallel implementations that can actually deliver high performance. The major challenges to scaling and efficiency include irregular data dependencies, poor locality, and high synchronization costs of current approaches. In addition to parallelism, researchers are developing approximation algorithms that use sampling for compressing and summarizing graph data. Streaming algorithms are also being considered for scenarios where the rate of updates is too fast to process the entire graph in a single pass. Further, out-of-core algorithms are necessary for massive graphs that do not fit in the main memory of a typical system. Researchers can use graph-based solutions for solving problems from many diverse disciplines, including routing and transportation, social networks, bioinformatics, computational science, health care, security and intelligence analysis.