  In this work, we use the theory of spatial networks to analyze galaxy
distributions. The aim is to develop new approaches to study the spatial galaxy
environment properties by means of the network parameters. We investigate how
each of the network parameters (degree, closeness and betweeness centrality;
diameter; giant component; transitivity) map the cluster structure and
properties. We measure the network parameters of galaxy samples comprising the
Coma Supercluster and 4 regions in their neighborhood ($z<0.0674$) using the
catalog produced by \citet{tempel2014flux}. For comparison we repeat the same
procedures for Random Geometric Graphs and Segment Cox process, generated with
the same dimensions and mean density of nodes. We found that there is a strong
correlation between degree centrality and the normalized environmental density.
Also, at high degrees there are more elliptical than spiral galaxies, which
confirms the density-morphology relation. The mean degree as a function of the
connection radius is an estimator of the count-of-spheres and consequently
provides the correlation dimension as a function of the connection radius. The
correlation dimension indicates high clustering at scales indicated by the
network diameter. Further, at this scales, high values of betweeness centrality
characterize galaxy bridges connecting dense regions, tracing very well the
filamentary structures. Then, since galaxies with the highest closeness
centrality belongs to the largest components of the network, associated to
supercluster regions, we can produce a catalog of superclusters only by
extracting the largest connected components of the network. Establishing the
correlation between the well-studied normalized environmental densities and the
parameters of the network theory allows us to develop alternative tools to the
study of the large-scale structures.
