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.

Navigability of temporal networks in hyperbolic space.

Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remains largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.