News & past events

New paper in Nature Physics

M. B. publications 03/11/2023

Geometric description of clustering in directed networks. We extend our geometric framework to describe real directed networks. The model is able to reproduce the spectrum of all types of directed triangles from real networks with astonishing accuracy.

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We are hiring

M. B. applications 04/10/2023

Postdoctoral positions in Network Science

The Mapping Complexity Lab of Prof. M. Ángeles Serrano and Prof. Marián Boguñá is opening a call to hire two postdoctoral researchers in the Department of Condensed Matter Physics, University of Barcelona.


A PhD in physics, computer science, computer/electronic engineering, mathematics, or other related disciplines.
Interest in interdisciplinary research, curiosity about AI and networks, high motivation to learn, an open-minded and collaborative spirit.
Excellent software development skills.
Excellent communication skills, and proficient in the English language, both written and spoken.


The successful applicant will work with Prof. M. Ángeles Serrano and Prof. Marián Boguñá in the foundations of complex networks and network geometry and/or at the interface between Network Science and Machine Learning. In this case, the goal is to merge the best of the two worlds to produce a new generation of models and methods for the classification and prediction of complex networks. We offer a 2-year position (1+1) with a competitive salary.

Application process:

Interested applicants are requested to submit a Curriculum Vitae including relevant publications and the name and contact details of 2 referees.

We promote diversity and equal opportunities, minorities in science are encouraged to apply.
Queries about this position should be sent to or

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New paper in Nature Communications

M. B. publications 16/10/2022

Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent  space is challenging but necessary to generate efficient embeddings to be used in a multitude of downstream tasks. Here, we propose a method to infer the dimensionality of networks without the need for any a priori spatial embedding. Due to the ability of hyperbolic geometry to capture the complex connectivity of real networks, we detect ultra low dimensionality far below values reported using other approaches. We applied our method to real networksfrom different domains and found unexpected regularities, including: tissue-specific biomolecular networks being extremely low dimensional; brain connectomes being close to the three dimensions of their anatomical embedding; and social networks and the Internet requiring slightly higher dimensionality. Beyond paving the way towards an ultra efficient dimensional reduction, our findings help address fundamental issues that hinge on dimensionality, such as universality in critical behavior. Read the paper here

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Cambridge Elements

M. B. publications 04/12/2021

A short introduction to the exciting field of network geometry.

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New paper in PNAS

M. B. publications 21/06/2021

Scaling up real networks by geometric branching growth

Branching processes underpin the complex evolution of manyreal systems. However, network models typically describe net-work growth in terms of a sequential addition of nodes. Here,we measured the evolution of real networks—journal cita-tions and international trade—over a 100-y period and foundthat they grow in a self-similar way that preserves their struc-tural features over time. This observation can be explained bya geometric branching growth model that generates a mul-tiscale unfolding of the network by using a combination ofbranching growth and a hidden metric space approach. Ourmodel enables multiple practical applications, including thedetection of optimal network size for maximal response to anexternal influence and a finite-size scaling analysis of criticalbehavior. Read the paper.

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Review on Network Geometry

M. B. publications 21/06/2021

Review on Network Geometry published in Nature Reviews Physics

Networks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others are the geometry of latent spaces underlying many networks and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale invariance, self-similarity and other forms of fundamental symmetries in networks. Network geometry is also of great use in a variety of practical applications, from understanding how the brain works to routing in the Internet. We review the most important theoretical and practical developments dealing with these approaches to network geometry and offer perspectives on future research directions and challenges in this frontier in the study of complexity. Read the paper.

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The physics of fun

M. Boguñá publications 05/11/2019

Engaging in playful activities, such as playing a musical instrument, learning a language, or per- forming sports, is a fundamental aspect of human life. We present a quantitative empirical analysis of the engagement dynamics into playful activities. We do so by analyzing the behavior of millions of players of casual video games and discover a scaling law governing the engagement dynamics. This power-law behavior is indicative of a multiplicative (i.e., happy- get-happier) mechanism of engagement characterized by a set of critical exponents. Read more

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