Signs of criticality in social explosions.

The success of an on-line movement could be defined in terms of the shift to large-scale and the later off-line massive street actions of protests. The role of social media in this process is to facilitate the transformation from small or local feelings of disagreement into large-scale social actions. The way how social media achieves that effect is by growing clusters of people and groups with similar effervescent feelings, which otherwise would not be in touch with each other. It is natural to think that these kinds of macro social actions, as a consequence of the spontaneous and massive interactions, will attain the growth and divergence of those clusters, like the correlation length of statistical physics, giving rise to important simplifications on several statistics. In this work, we report the presence of signs of criticality in social demonstrations. Namely, similar power-law exponents are found whenever the distributions are calculated either considering time windows of the same length or with the same number of hashtag usages. In particular, the exponents for the distributions during the event were found to be smaller than before the event, and this is also observed either if we count the hashtags only once per user or if all their usages are considered. By means of network representations, we show that the systems present two kinds of high connectedness, characterised by either high or low values of modularity. The importance of analysing systems near a critical point is that any small disturbance can escalate and induce large-scale-nationwide-chain reactions.

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.

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.