Network analysis is useful in modeling the structures of different phenomena. A fundamental question in the analysis of network data is whether a network contains community structure. One type of community structure of interest is a dense subgraph. Statistically deciding whether a network contains a dense subgraph can be formulated as a hypothesis test where under the null hypothesis, there is no community structure, and under the alternative hypothesis, the network contains a dense subgraph. One method in performing this hypothesis test is by counting the frequency of shapes created by all three-node subgraphs. In this study, three different test statistics based on the frequency of three-node subgraph shapes will be compared in their ability to detect a dense subgraph in simulated networks of varying size and characteristics.