Fabio Saracco — ISC-CNR Roma #
Randomizing bipartite networks: the case of the World Trade Web #
The class of networks represented by bipartite networks has been recognized to provide a particularly 
insightful representation of many different systems: ecological networks, trade networks, citations and 
collaboration networks represent only few examples. Anyway, quite surprisingly, little work has been done so 
far to implement null models on real bipartite networks. In particular, null models for bipartite networks 
proposed so far show several limitations, ranging from being purely numerical (thus lacking the analytic 
character), to assuming an a priori functional form either for the distribution of the quantities of interest 
or for the model’s parameters (thus not being real data-rooted) or, lastly, using approximate analytical 
models. In this paper, we propose a theoretical framework guaranteeing the three aforementioned properties, 
extending a recently-proposed method to randomize monopartite networks to bipartite networks. The method rests 
upon the sequential maximization of Shannon entropy and the likelihood function, a combination which has been 
proven to be highly effective both for detecting patterns and to reconstruct the structure of several 
real-world networks. While the proposed formalism is perfectly general, in this paper we apply our method to 
the binary, undirected, bipartite representation of the World Trade Web, as described by two different data 
sets (1963-2000 and 1995-2010). We extend the definition of several monopartite quantities of interest to the 
bipartite case and compare the output of our null model with the observed trends. Such a comparison shows that 
the bipartite WTW behaves completely differently from the monopartite WTW. Remarkably, the bipartite definition 
of the closed motifs (here proposed for the first time), allows us to detect early-warning signals of the 
2007-2008 crisis (dating back to 2003) witnessed by the increasing level of randomness of the observed network 
structure. Moreover, signals of the crisis attenuation after 2007 seem to be visible.