We study graph properties , such as diameter, density and clustering coefficients,  and the relationships between these graph properties . Whereas for graphs on small number of vertices  we can exactly compute the average values and range for each property of interest, this becomes infeasible for larger graphs. 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. We also }  use linear and non-linear models to predict a specific property based on the other properties .
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 Erdos-R\'enyi graph generator with p = 1/2 models well the underlying graph space of all labeled graphs with fixed number of vertices s-R\'enyi model and compare the results with known theoretical bounds, where applicable. We also } , 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 .
R
graph properties
properties of labeled graphs
D
diameter, density and
A
centrality measures, spectral radius, degree assortativity,
R
between these graph properties
and correlations between them. Specifically, we consider twelve properties of interest in the graph theoretical and the graph mining literature
A
(4, 5, 6, 7)
R
Thus, we analyze graph properties and the relationships between the properties using
We experimentally show that graphs generated by the
R
graphs, which model
graph generator with p = 1/2 models
R
. Specifically, we focus on thirteen properties of interest in graph theory and graph mining. We numerically study the behavior of these properties, as the
of all labeled graphs with fixed
D
increase, for the Erd\H{o
A
, allowing us to study larger graphs and analyze their properties and correlations between these properties. We
R
specific
given
R
other properties
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