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Many real-world complex systems consist of a set of elementary units connected by relationships of different kinds. All such systems are better described in terms of multiplex networks, where the links at each layer represent a different type of interaction between the same set of nodes rather than in terms of (single-layer) networks. In this paper we present a general framework to describe and study multiplex networks, whose links are either unweighted or weighted. In particular, we propose a series of measures to characterize the multiplexicity of the systems in terms of (i) basic node and link properties such as the node degree, and the edge overlap and reinforcement, (ii) local properties such as the clustering coefficient and the transitivity, and (iii) global properties related to the navigability of the multiplex across the different layers. The measures we introduce are validated on a genuinely multiplex data set of Indonesian terrorists, where information among 78 individuals are recorded with respect to mutual trust, common operations, exchanged communications, and business relationships.

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Although multilevel sociality is a universal feature of human social organization, its functional relevance remains unclear. Here, we investigated the effect of multilevel sociality on cumulative cultural evolution by using wireless sensing technology to map inter- and intraband social networks among Agta hunter-gatherers. By simulating the accumulation of cultural innovations over the real Agta multicamp networks, we demonstrate that multilevel sociality accelerates cultural differentiation and cumulative cultural evolution. Our results suggest that hunter-gatherer social structures [based on (i) clustering of families within camps and camps within regions, (ii) cultural transmission within kinship networks, and (iii) high intercamp mobility] may have allowed past and present hunter-gatherers to maintain cumulative cultural adaptation despite low population density, a feature that may have been critical in facilitating the global expansion of Homo sapiens.

We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in groups of more than two players. Here, we study the evolutionary dynamics of a public goods game in social systems with higher-order interactions. First, we show that the game on uniform hypergraphs corresponds to the replicator dynamics in the well-mixed limit, providing a formal theoretical foundation to study cooperation in networked groups. Secondly, we unveil how the presence of hubs and the coexistence of interactions in groups of different sizes affects the evolution of cooperation. Finally, we apply the proposed framework to extract the actual dependence of the synergy factor on the size of a group from real-world collaboration data in science and technology. Our work provides a way to implement informed actions to boost cooperation in social groups.