  We investigate the fundamental statistical features of tagged (or annotated)
networks having a rich variety of attributes associated with their nodes. Tags
(attributes, annotations, properties, features, etc.) provide essential
information about the entity represented by a given node, thus, taking them
into account represents a significant step towards a more complete description
of the structure of large complex systems. Our main goal here is to uncover the
relations between the statistical properties of the node tags and those of the
graph topology. In order to better characterise the networks with tagged nodes,
we introduce a number of new notions, including tag-assortativity (relating
link probability to node similarity), and new quantities, such as node
uniqueness (measuring how rarely the tags of a node occur in the network) and
tag-assortativity exponent. We apply our approach to three large networks
representing very different domains of complex systems. A number of the tag
related quantities display analogous behaviour (e.g., the networks we studied
are tag-assortative, indicating possible universal aspects of tags versus
topology), while some other features, such as the distribution of the node
uniqueness, show variability from network to network allowing for pin-pointing
large scale specific features of real-world complex networks. We also find that
for each network the topology and the tag distribution are scale invariant, and
this self-similar property of the networks can be well characterised by the
tag-assortativity exponent, which is specific to each system.
