Before revision:  Thus, we analyze graph properties and the relationships between the properties using Erdos-R\'enyi graphs, which model well the underlying graph space . Specifically, we focus on thirteen properties of interest in graph theory and graph mining. We numerically study the behavior of these properties, as the number of vertices increase, for the Erd\H{os-R\'enyi model and compare the results with known theoretical bounds, where applicable.
After revision:  Thus, we analyze graph properties and the relationships between the properties using Erdos-R\'enyi graphs, which model well the underlying graph space of all labeled graphs with fixed number of vertices increase, for the Erd\H{os-R\'enyi model and compare the results with known theoretical bounds, where applicable.