  Quantification of symmetries in complex networks is typically done globally
in terms of automorphisms. Extending previous methods to locally assess the
symmetry of nodes is not straightforward. Here we present a new framework to
quantify the symmetries around nodes, which we call connectivity patterns. We
develop two topological transformations that allow a concise characterization
of the different types of symmetry appearing on networks and apply these
concepts to six network models, namely the Erd\H{o}s-R\'enyi,
Barab\'asi-Albert, random geometric graph, Waxman, Voronoi and rewired Voronoi.
Real-world networks, namely the scientific areas of Wikipedia, the world-wide
airport network and the street networks of Oldenburg and San Joaquin, are also
analyzed in terms of the proposed symmetry measurements. Several interesting
results emerge from this analysis, including the high symmetry exhibited by the
Erd\H{o}s-R\'enyi model. Additionally, we found that the proposed measurements
present low correlation with other traditional metrics, such as node degree and
betweenness centrality. Principal component analysis is used to combine all the
results, revealing that the concepts presented here have substantial potential
to also characterize networks at a global scale.
