Many complex systems present an intrinsic bipartite structure where elements of one set link to elements of the second set. In these complex systems, such as the system of actors and movies, elements of one set are qualitatively different than elements of the other set. The properties of these complex systems are typically investigated by constructing and analyzing a projected network on one of the two sets (for example the actor network or the movie network). Complex systems are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set, and this heterogeneity makes it very difficult to discriminate links of the projected network that are just reflecting system's heterogeneity from links relevant to unveil the properties of the system. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis that takes into account system heterogeneity. We apply the method to a biological, an economic and a social complex system. The method we propose is able to detect network structures which are very informative about the organization and specialization of the investigated systems, and identifies those relationships between elements of the projected network that cannot be explained simply by system heterogeneity. We also show that our method applies to bipartite systems in which different relationships might have different qualitative nature, generating statistically validated networks in which such difference is preserved.

We investigate the emergence of a structure in the correlation matrix of assets’ returns as the time horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New York, Paris, London, Milano) and with different methods. In addition to the usual correlations, we also analyze those obtained by subtracting the dynamics of the “center of mass” (i.e., the market mode). We find that when the center of mass is not removed the structure emerges, as the time horizon increases, from splitting a single large cluster into smaller ones. By contrast, when the market mode is removed the structure of correlations observed at the daily scale is already well defined at very high frequency ($5\min$ in the New York Stock Exchange). Moreover, this structure accounts for 80% of the classification of stocks in economic sectors. Similar results, though less sharp, are found for the other markets. We also find that the structure of correlations in the overnight returns is markedly different from that of intraday activity.

We investigate the trading behaviour of a large set of single investors trading the highly liquid Nokia stock over the period 2003–2008 with the aim of determining the relative role of endogenous and exogenous factors that may affect their behaviour. As endogenous factors, we consider returns and volatility, whereas the exogenous factors are the total daily number of news articles and a semantic variable based on a sentiment analysis of the news. Linear regression and partial correlation analysis of the data show that different categories of investors are differently correlated to these factors. Governmental and non-profit organizations are weakly sensitive to news and returns or volatility, and, typically, they are more correlated with the former than with the latter. Households and companies, on the contrary, are very sensitive to both endogenous and exogenous factors, and volatility and returns are, on average, much more relevant than the number of news articles and sentiment, respectively. Financial institutions and foreign organizations are intermediate between these two cases, in terms of both the total explanatory power of these factors and their relative importance. We explicitly consider the role of overnight news and overnight returns on the successive trading activity and trading balance of the different categories of investors. We observe the role of the overnight news, which is weaker than the ones observed between synchronous variables. By performing a vector autoregression (VAR) analysis, we show that the flux of news of the previous day affects the trading activity of companies, households and foreign investors and the dynamics of volatility. VAR is not detecting any role of the lagged sentiment in the successive values of the difference between the number of buying and selling investors for each category of investors