Machine learning and network geometry

I am currently exploring how machine learning techniques can help to better understand latent spaces that underlie observed topologies of real networks. In particular, I am interesting in bringing together model free approaches from machine learning with theoretical models of networks embedded in metric spaces.

Evolution and competition of online social networks

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Online social networks have grown rapidly in the last decade. We have revealed the main mechanisms responsible for the evolution of their topology [PRX 4, 031046], explain why and when several online social networks can coexist while competing for the attention of users (digital ecology) [Sci. Rep. 5, 10268], and how an international network like Facebook can win or loose against local networks [Sci. Rep. 6, 25116].

Current research questions include how networks with different intrinsic fitnesses compete, how a later launched but better network can win, and what initial marketing initiatives can achieve.

Geometry of multiplex networks

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Heterogeneous clustered networks can be embedded into underlying hyperbolic metric spaces that comprise a popularity (degree) and similarity dimension. We have generalized this framework to multiplex networks, which consist of several networking layers in which the same nodes are present (but the layer topologies can differ). We have found that real multiplex networks exhibit significant geometric correlations, and these correlations allow for trans-layer link prediction, can facilitate community detection, and if they are strong (but not too strong) they improve navigation [Nat. Phys. 12, 1076–1081]. Whereas it is well known that degree correlations increase the robustness of multiplexes against random failures (percolation), we have shown that correlations in the similarity dimension improve their robustness against targeted attacks, where one removes nodes ordered by their degree [PRL 118, 218301]. See also this infographic.

Future research questions include how geometric correlations impact different dynamical processes taking place on the multiplex as well as how to generalize the framework to deal with general multilayer networks that encode interdependencies between different entities.

Evolutionary game theory and pattern formation on networks


The interplay between nonlinear dynamics and spatial effects often leads to the formation of patterns. Such patterns unfolding in Euclidean space have been shown to promote cooperation in social dilemmas on lattices, whereas it is also well known that heterogeneous network structures promote cooperation. We have shown that in heterogeneous (scale-free) networks, similar dynamical patterns emerge in latent hyperbolic spaces underlying these topologies*. Importantly, for a high mean local clustering these patterns are more important to sustain cooperation than the most connected nodes, and in this case more heterogeneity can even hinder cooperation [Nat. Comm. 8, 1888]. The formation of patterns is also important in promoting the collective navigation of networks embedded into hyperbolic space [Sci. Rep. 7, 2897]. In multiplex networks, similar patterns can be found overlapping in different layers if geometric correlations are present [Sci. Rep. 7, 7087]. Furthermore, popularity (degree) correlations can lead to topological enslavement where an encrusted society emerges that is insensitive to incentives (payoffs) [NJP 20, 053030].

Current research questions include how similar patterns can emerge from a broad range of dynamical processes and how effective incentives can be designed to deal with various urgent societal challenges [EPJ ST 225:3231].

*: see