We study properties of labeled graphs, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, and the relationships and correlations between them. Specifically, we consider twelve properties of interest in the graph theoretical and the graph mining literature... Whereas for graphs on small number of vertices (4, 5, 6, 7) we can exactly compute the average values and range for each property of interest, this becomes infeasible for larger graphs. We experimentally show that graphs generated by the Erd\H{o}s-R\'enyi graph generator with p = 1/2 models well the underlying graph space of all labeled graphs with fixed number of vertices, allowing us to study larger graphs and analyze their properties and correlations between these properties. We use linear and non-linear models to predict a given property based on the others and find the most predictive subset. We also develop a model to classify graphs obtained by different graph generators and again identify the most predictive subset of properties. For both experiments the results show that pairs and triples of properties have high predictive power. (read more)