Structure of the Region-Technology Network as a Driver for Technological Innovation.

Agglomeration and spillovers are key phenomena of technological innovation, driving regional economic growth. Here, we investigate these phenomena through technological outputs of over 4,000 regions spanning 42 countries, by analyzing more than 30 years of patent data (approximately 2.7 million patents) from the European Patent Office. We construct a bipartite network-based on revealed comparative advantage-linking geographic regions with areas of technology and compare its properties to those of artificial networks using a series of randomization strategies, to uncover the patterns of regional diversity and technological ubiquity. Our results show that the technological outputs of regions create nested patterns similar to those of ecological networks. These patterns suggest that regions need to dominate various technologies first (those allegedly less sophisticated), creating a diverse knowledge base, before subsequently developing less ubiquitous (and perhaps more sophisticated) technologies as a consequence of complementary knowledge that facilitates innovation. Finally, we create a map-the Patent Space Network-showing the interactions between technologies according to their regional presence. This network reveals how technology across industries co-appear to form several explicit clusters, which may aid future works on predicting technological innovation due to agglomeration and spillovers.

Transitivity and degree assortativity explained: The bipartite structure of social networks.

Dynamical processes, such as the diffusion of knowledge, opinions, pathogens, "fake news," innovation, and others, are highly dependent on the structure of the social network in which they occur. However, questions on why most social networks present some particular structural features, namely, high levels of transitivity and degree assortativity, when compared to other types of networks remain open. First, we argue that every one-mode network can be regarded as a projection of a bipartite network, and we show that this is the case using two simple examples solved with the generating functions formalism. Second, using synthetic and empirical data, we reveal how the combination of the degree distribution of both sets of nodes of the bipartite network-together with the presence of cycles of lengths four and six-explain the observed values of transitivity and degree assortativity coefficients in the one-mode projected network. Bipartite networks with top node degrees that display a more right-skewed distribution than the bottom nodes result in highly transitive and degree assortative projections, especially if a large number of small cycles are present in the bipartite structure.

Degree distributions of bipartite networks and their projections.

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.

Look who's talking: Two-mode networks as representations of a topic model of New Zealand parliamentary speeches.

Quantitative methods to describe the participation to debate of Members of Parliament and the parties they belong to are lacking. Here we propose a new approach that combines topic modeling with complex networks techniques, and use it to characterize the political discourse at the New Zealand Parliament. We implement a Latent Dirichlet Allocation model to discover the thematic structure of the government's digital database of parliamentary speeches, and construct from it two-mode networks linking Members of the Parliament to the topics they discuss. Our results show how topic popularity changes over time and allow us to relate the trends followed by political parties in their discourses with specific social, economic and legislative events. Moreover, the community analysis of the two-mode network projections reveals which parties dominate the political debate as well as how much they tend to specialize in a small or large number of topics. Our work demonstrates the benefits of performing quantitative analysis in a domain normally reserved for qualitative approaches, providing an efficient way to measure political activity.