  An adjacency labeling scheme is a method that assigns labels to the vertices
of a graph such that adjacency between vertices can be inferred directly from
the assigned label, without using a centralized data structure. We devise
adjacency labeling schemes for the family of power-law graphs. This family that
has been used to model many types of networks, e.g. the Internet AS-level
graph. Furthermore, we prove an almost matching lower bound for this family. We
also provide an asymptotically near- optimal labeling scheme for sparse graphs.
Finally, we validate the efficiency of our labeling scheme by an experimental
evaluation using both synthetic data and real-world networks of up to hundreds
of thousands of vertices.
