  Many real-world complex networks are best modeled as bipartite (or 2-mode)
graphs, where nodes are divided into two sets with links connecting one side to
the other. However, there is currently a lack of methods to analyze properly
such graphs as most existing measures and methods are suited to classical
graphs. A usual but limited approach consists in deriving 1-mode graphs (called
projections) from the underlying bipartite structure, though it causes
important loss of information and data storage issues. We introduce here
internal links and pairs as a new notion useful for such analysis: it gives
insights on the information lost by projecting the bipartite graph. We
illustrate the relevance of theses concepts on several real-world instances
illustrating how it enables to discriminate behaviors among various cases when
we compare them to a benchmark of random networks. Then, we show that we can
draw benefit from this concept for both modeling complex networks and storing
them in a compact format.
