News & past events (40)  pag. 1

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

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

Cambridge Elements

M. B. publications 04/12/2021

A short introduction to the exciting field of network geometry.

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.

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.

The physics of fun

M. BoguƱƔ 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

Postdoctoral position available (closed)

M. B. applications 19/06/2018

Postdoctoral Position, Mapping Big Data Systems

Applications are invited for a Postdoctoral fellowship at the University of Barcelona to work with Prof. M. Ángeles Serrano and Prof. Marián Boguñá at the Department of Condensed Matter Physics and UB Institute of Complex Systems (UBICS). The position is funded by a "Fundación BBVA" grant.

This is a postdoctoral position with a salary of €29,700 per year (before taxes) for one year renewable until june 2020. There will be additional support for conference travels.

The topic:

The discovery and understanding of the hidden geometry of complex networks have become fundamental problems within Network Science giving place to the field of Network Geometry. The research will focus on mixing of machine learning and statistical techniques for an efficient embedding of very large networks in hidden metric spaces to produce meaningful maps. We will create an online platform to host an atlas of network maps, and where scientists and interested people can produce theirs.

Essential Skills:

- A PhD in Physics, Computer Science, Computer/Electronic Engineering, or other relevant discipline is expected.
- Expertise in complex networks
- Excellent software development skills
- Excellent communication skills, verbal and written (English)

Informal queries about this position should be sent to

Application process:

Interested applicants are requested to submit

- a Curriculum Vitae including relevant publications and the name and contact details of 2 referees

- a one page cover letter explaining your interest in this specific position

Submissions should be sent by email with subject “MBDS Application” to

Interviews will be carried out as soon as suitable candidates are identified.

To successful candidate is expected to start in September  2018, or before (if possible).

New paper in Nature Physics. Renormalization Group for Complex Networks

M. BoguƱƔ publications 21/03/2018

We use the geometry underlying real complex networks to define a renormalization group. Check the paper here

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macfang workshops 06/11/2017

Mapping Complexity. Foundations and Applications of Network Geometry
Barcelona | November 6 – 8, 2017

Full details can be found at our website We kindly ask for your cooperation in spreading the word by forwarding this e-mail and retweeting our posts @macfang17. Hope to meet you next November in Barcelona!

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World Trade Atlas 1870-2013

M. BoguƱƔ applications 01/03/2017

We present the World Trade Atlas 1870-2013, a collection of annual world trade maps in which distances incorporate the different dimensions that affect international trade, beyond mere geography. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat, but hyperbolic. You can check the evolution of world trade in this interactive video tool

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New paper in Nature Communications

Nature Physics Research Highlights, A. Klopper publications 01/03/2017

The old maxim that it's less about what you know than who you know is an appropriate analogy for how the behaviour of a complex network can be profoundly influenced by the weights of its links. Read more

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New paper in Nature Physics

M BoguƱƔ publications 01/02/2017

We show that multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers.

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Postdoctoral position available (closed)

redacciĆ³n advices 06/03/2015

We invite applications for a Post-Doctoral Research Associate (1+1 years) in Network Science-Mapping Complexity at the University of Barcelona (Spain). The successful candidate will be required to join us in the investigation of complex networks embedded in hidden metric spaces to get insights into the connection between the structure and function in biological complex systems.

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Postdoctoral position available (closed)

M. BoguƱƔ advices 10/11/2014

Universitat de Barcelona announces the availability of one Marie-Curie experienced researcher position in Online Social Networking technologies with a focus on structure and evolution of social networks and their navigability properties (code: iSocial-UB-ER4)

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Complex architecture of primes and natural numbers

NewScientist publications 08/10/2014

Is there a pattern behind prime numbers? This is one of the biggest questions in mathematics. Now networks that reproduce relationships between primes and non-primes could point the way to an answer. Read the paper.

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New paper in Physical Review X

Phys. Rev. X publications 29/09/2014

Online social networks offer a data-driven way to study patterns of human behavior on small and large scales. Researchers have shown that individuals are significantly more likely to enroll in social networks based on the influence of one active friend than the influence of mass-media campaigns. Read the paper. Check the videos here and here

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New paper in Phyical Review X

M. BoguƱƔ publications 28/05/2014

Strong clustering in networks induces a core-periphery organization responsible for the emergence of a double percolation transition associated with the same symmetry breaking.

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Mapping complexity: Embedding networks in hidden metric spaces

M. BoguƱƔ awards 05/12/2013

M. Ángeles Serrano and Marián Boguñá have been awarded a 21st Century Science Initiative Grant: Studying Complex Systems of the James S. McDonnell Foundation.

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Cosmological networks

M. BoguƱƔ projects 24/10/2013

The causal structure of observers uniformly scattered in an open FLRW universe is a growing scale-free network

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New postdoctoral positions (closed)

M. BoguƱƔ advices 17/10/2013

Two post-doctoral research associate positions (1+1 years) are available at the University of Barcelona to work on the field of complex networks/network science

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New paper in Scientific Reports

M. BoguƱƔ publications 30/08/2013

Degree distribution and degree-dependent clustering coefficient alone seem to be responsible for the emergence of the global organization of complex networks.

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New paper in Physical Review Letters

M. BoguƱƔ publications 20/08/2013

Yet another paper on the existence/non-existence of an epidemic threshold in the SIS model. It seems that our colleagues Lee et al. do not believe our results. Read their comment here and our reply here

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European Conference on Complex Systems 2013

M. BoguƱƔ conferences 20/08/2013

Don't miss this exciting conference that will take place in Barcelona, 16-20 September 2013. On Monday 16, I will give an invited talk entitled "Hyperbolic Geometry of Complex Networks"

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Joint CRM-Imperial College school and workshop in complex systems

M. BoguƱƔ news 21/01/2013

A three hours course on Percolation in Complex Networks. April 8 to 13 2013.

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