  We develop graphlet analysis for multiplex networks and discuss how this
analysis can be extended to multilayer and multilevel networks as well as to
graphs with node and/or link categorical attributes. The analysis has been
adapted for two typical examples of multiplexes: economic trade data
represented as a 957-plex network and 75 social networks each represented as a
12-plex network. We show that wedges (open triads) occur more often in economic
trade networks than in social networks, indicating the tendency of a country to
produce/trade of a product in local structure of triads which are not closed.
Moreover, our analysis provides evidence that the countries with small
diversity tend to form correlated triangles. Wedges also appear in the social
networks, however the dominant graphlets in social networks are triangles
(closed triads). If a multiplex structure indicates a strong tie, the graphlet
analysis provides another evidence for the concepts of strong/weak ties and
structural holes. In contrast to Granovetter's seminal work on the strength of
weak ties, in which it has been documented that the wedges with only strong
ties are absent, here we show that for the analyzed 75 social networks, the
wedges with only strong ties are not only present but also significantly
correlated.
