Understanding who talks about what: comparison between the information treatment in traditional media and online discussions.

We study the dynamics of interactions between a traditional medium, the New York Times journal, and its followers in Twitter, using a massive dataset. It consists of the metadata of the articles published by the journal during the first year of the COVID-19 pandemic, and the posts published in Twitter by a large set of followers of the @nytimes account along with those published by a set of followers of several other media of different kind. The dynamics of discussions held in Twitter by exclusive followers of a medium show a strong dependence on the medium they follow: the followers of @FoxNews show the highest similarity to each other and a strong differentiation of interests with the general group. Our results also reveal the difference in the attention payed to U.S. presidential elections by the journal and by its followers, and show that the topic related to the "Black Lives Matter" movement started in Twitter, and was addressed later by the journal.

Socioeconomic correlations and stratification in social-communication networks.

The uneven distribution of wealth and individual economic capacities are among the main forces, which shape modern societies and arguably bias the emerging social structures. However, the study of correlations between the social network and economic status of individuals is difficult due to the lack of large-scale multimodal data disclosing both the social ties and economic indicators of the same population. Here, we close this gap through the analysis of coupled datasets recording the mobile phone communications and bank transaction history of one million anonymized individuals living in a Latin American country. We show that wealth and debt are unevenly distributed among people in agreement with the Pareto principle; the observed social structure is strongly stratified, with people being better connected to others of their own socioeconomic class rather than to others of different classes; the social network appears to have assortative socioeconomic correlations and tightly connected 'rich clubs'; and that individuals from the same class live closer to each other but commute further if they are wealthier. These results are based on a representative, society-large population, and empirically demonstrate some long-lasting hypotheses on socioeconomic correlations, which potentially lay behind social segregation, and induce differences in human mobility.

Deciphering the global organization of clustering in real complex networks.

We uncover the global organization of clustering in real complex networks. To this end, we ask whether triangles in real networks organize as in maximally random graphs with given degree and clustering distributions, or as in maximally ordered graph models where triangles are forced into modules. The answer comes by way of exploring m-core landscapes, where the m-core is defined, akin to the k-core, as the maximal subgraph with edges participating in at least m triangles. This property defines a set of nested subgraphs that, contrarily to k-cores, is able to distinguish between hierarchical and modular architectures. We find that the clustering organization in real networks is neither completely random nor ordered although, surprisingly, it is more random than modular. This supports the idea that the structure of real networks may in fact be the outcome of self-organized processes based on local optimization rules, in contrast to global optimization principles.

Dynamical collision network in granular gases.

We address the problem of recollisions in cooling granular gases. To this aim, we dynamically construct the interaction network in a granular gas, using the sequence of collisions collected in an event driven simulation of inelastic hard disks from time 0 until time t . The network is decomposed into its k -core structure: particles in a core of index k have collided at least k times with other particles in the same core. The difference between cores k+1 and k is the so-called k -shell, and the set of all shells is a complete and nonoverlapping decomposition of the system. Because of energy dissipation, the gas cools down: its initial spatially homogeneous dynamics, characterized by the Haff law, i.e., a t{-2} energy decay, is unstable toward a strongly inhomogeneous phase with clusters and vortices, where energy decays as t{-1} . The clear transition between those two phases appears in the evolution of the k -shells structure in the collision network. In the homogeneous state the k -shell structure evolves as in a growing network with a fixed number of vertices and randomly added links: the shell distribution is strongly peaked around the most populated shell, which has an index k{max} approximately 0.9(d) with (d) the average number of collisions experienced by a particle. During the final nonhomogeneous state a growing fraction of collisions is concentrated in small, almost closed, communities of particles: k{max} is no more linear in (d) and the distribution of shells becomes extremely large developing a power-law tail approximately k{-3} for high shell indexes. We conclude proposing a simple algorithm to build a correlated random network that reproduces, with few essential ingredients, the whole observed phenomenology, including the t{-1} energy decay. It consists of two kinds of collisions (links): single random collisions with any other particle and long chains of recollisions with only previously encountered particles. The algorithm disregards the exact spatial arrangement of clusters, suggesting that the observed stringlike structures are not essential to determine the statistics of recollisions and the energy decay.