  Bipartite (two-mode) networks are important in the analysis of social and
economic systems as they explicitly show conceptual links between different
types of entities. However, applications of such networks often work with a
projected (one-mode) version of the original bipartite network. The topology of
the projected network, and the dynamics that take place on it, are highly
dependent on the degree distributions of the two different node types from the
original bipartite structure. To date, the interaction between the degree
distributions of bipartite networks and their one-mode projections is well
understood for only a few cases, or for networks that satisfy a restrictive set
of assumptions. Here we show a broader analysis in order to fill the gap left
by previous studies. We use the formalism of generating functions to prove that
the degree distributions of both node types in the original bipartite network
affect the degree distribution in the projected version. To support our
analysis, we simulate several types of synthetic bipartite networks using a
configuration model where node degrees are assigned from specific probability
distributions, ranging from peaked to heavy-tailed distributions. Our findings
show that when projecting a bipartite network onto a particular set of nodes,
the degree distribution for the resulting one-mode network follows the
distribution of the nodes being projected on to, but only so long as the degree
distribution for the opposite set of nodes does not have a heavier tail.
Furthermore, we show that bipartite degree distributions are not the only
feature driving topology formation of projected networks, in contrast to what
is commonly described in the literature.
