Complexity Lab Barcelona

Foundations of Complex Networks

M. Ángeles Serrano and Marián Boguñá

A wide class of real systems of many interacting elements can be mapped into graphs or networks. Under this approach, vertices or nodes of the network represent the elements of the system whereas edges or links among them stand for interactions between different elements. This mapping has triggered a huge number of works and a surge of interest in the field of complex networks that has lead to a general framework within which to analyze their topology as well as the dynamical processes running on top of them.

In many cases, these dynamical processes are directly related to functionality and involve some kind of transport or traffic flow. Furthermore, the very existence of those networks could be naturally explained as a direct consequence of the communication need among its constituents. The Internet or the World Wide Web are clear examples. In order to preserve functionality, networks characterized by transport processes must be connected, that is, a path must exist between any pair of nodes, or, at least, there must exist a macroscopic portion of vertices --or giant component-- able to communicate. In this context, percolation theory appears as an indispensable tool to analyze the conditions under which such connected structures emerge in large networks.

Our research in this field is focused towards the study of structural properties of networks and new percolation phenomena, such as percolation in random directed networks with one and two points degree correlations, bidirectional connections and clustering. These are ubiquitous properties in the networks of the real life which have strong implications in their percolation properties.

Learn more about it in: Mapping Complexity Lab

Citizen Science for Computational Social Science

Josep Perelló

Under the name of Citizen Science, many innovative practices in which volunteers partner with scientist to pose and answer real-world questions are quickly growing worldwide. Citizen Science can furnish ready made solutions with the active role of citizens. We particularly bridge Computational Social Sciences with Citizen Science philosophy, which in our case takes the form of what we call Pop-Up Experiments: Non-permanent, highly participatory collective experiments which blend features developed by Big Data methodologies and Behavioural Experiments protocols with ideals of Citizen Science.

Our methodology is based on community processes that seek to make the city and urban environments an open lab and we do it through OpenSystems platform. We are committed to multidisciplinary and horizontal research, innovation and public engagement. Our research also incorporates artists into scientific groups, in a stable and fruitful way, so that they can be important pieces in the new knowledge generation process.

We mostly include topics such as: Urban and Cultural Spaces Human Mobility, Sensors and Environment, Games and Human Behaviour.

We coordinate the Barcelona Citizen Science Office (an initiative with Barcelona City Council), we have received a RecerCaixa grant to improve the mechanisms to make possible citizen science projects and we are founding members of the European Citizen Science Association.

Learn more about it in: OpenSystems

Synchronization in Complex Networks

Albert Díaz-Guilera

Complexity is usually understood as the emergence of nontrivial collective behaviors from the dynamical evolution of simple units that are interconnected. Synchronization corresponds to a global behavior of a population of individual oscillators. We have basically analyzed the influence of the topological features of complex networks in the dynamical properties of the system.

Learn more about it in: CEPS (Collective Emergent Phenomena in Physical Systems)

Renormalization of Complex Networks

M. Ángeles Serrano and Marián Boguñá

Renormalization is a powerful framework to explore physical systems across length scales. In statistical physics, it has been highly successful in explaining universal properties of phase transitions, leading to the concepts of universality and scale invariance. However, the small-world property and heterogeneity of complex networks complicate the application of the renormalization group by introducing correlations between coexisting scales.

Our geometric renormalization framework for investigating complex networks across length scales is based on our discovery that the structure of complex networks is underlain by a latent hyperbolic geometry. In this hidden metric space, nodes have coordinates defining distances that determine the likelihood of interaction via a universal gravity-like or Fermi-like connectivity law. This law operates at all length scales, simultaneously encodes short- and long-range connections.

Using this geometric principle, we have established a family of geometric network models that explain many prominent features of the structure of real networks. We have also developed embedding methods that generate a geometric representation of a real network consistent with its connectivity structure. Based on these maps, geometric renormalization (GR) techniques can be applied to explore the structure of real networks at different length scales.

Geometric renormalization applies a scale transformation that coarse-grains and rescales a network representation in the hyperbolic plane. The result is the multiscale unfolding of a network over progressively longer length scales. This transformation has revealed that self-similarity is a ubiquitous symmetry in the structure of real networks, from the Internet to biological networks in the cell. It explains the scale invariance observed in human multiscale brain connectomes reconstructed from anatomical data. Additionally, the growth over time of some real networks also exhibits self-similarity, such as the journal citation network and the world trade web. Their evolution can be modeled using a fine-graining or reverse renormalization process that sustains a novel class of growing network models based on a node branching process and inheritance.

Practical applications of our GR techniques include scaled-up and scaled-down replicas of real networks.

Learn more about it in: Mapping Complexity Lab

Biological Networks

M. Ángeles Serrano

We are interested in brain networks, more specifically in understanding how spatial constraints shape their organization, development and function. We also study networks of molecular interactions in the cell. In the long term, we aim at producing a whole-cell functional network integrating signalling, genome, epigenome, proteome, and metabolism to mimic observed phenotypes and to predict cellular responses.

Learn more about it in: Mapping Complexity Lab

Economic Networks

M. Ángeles Serrano

International trade moves annually trillions of dollars and represents one of the main networks of interactions between countries in the world. Along economic size, geographic distance has been recognized to shape trade interactions but its importance is currently under scrutiny. The gravity theory of trade flows is directly related with the connection probability we use in our hidden metric space models. We plan to map the world trade web according not only to geographic location but to actual aggregated barriers to international trade in the world.

World Trade Atlas 1870-2013

Learn more about it in: Mapping Complexity Lab

Epidemic Spreading

Marián Boguñá and M. Ángeles Serrano

Networks are often the substrate over which spreading processes take place. Our research in this area is mainly focused on the understanding of the interplay between the network structure and spreading dynamics.

Learn more about it in: Mapping Complexity Lab

Human Behavior and Decision Making

Josep Perelló

We investigate the behaviour of each individual in relation to his own benefit and the collective benefit. We use the infrastructure of the Board Games Festival DAU Barcelona to empirically find answers about humans’ behaviour through games and social dilemmas. We develop and design on digital platforms collective experiments to follow the humans’ decision making. The first experiment of this project was conducted during the DAU in Fabra i Coats (Barcelona, 15 and 16 December 2012). The experiment is based on a model of conflicts that has been studied in detail to model, analyse and/or solve many real world situations: the prisoner's dilemma. In the next edition (14 and 15 December 2013), we developed "Mr. Banks, the stock exchange game". Based on information related to the financial markets, the participants were asked if they think that the market will rise or fall. In 2014, we proposed a new character called Dr. Brain, to study human behavior in an ample suite of games: prisoner's dilemma, harmony, stag-hunt and snowdrift games. We there explored the behaviour of subjects accross these ample collection of social dilemmas.

Learn more about it in: OpenSystems

Human Mobility

Albert Diaz-Guilera

The increased pervasiveness of information and communication technologies is enabling the tracking of human mobility at an unprecedented scale. Massive call detail records from mobile phone activities and the use of global positioning systems (GPS) in large vehicle fleets for instance, are generating extraordinary quantities of positional and movement data available for researchers who aim to understand human activity in space. Other data sources, such as observations of banknote circulation, online location-based social networks, radio frequency identification traces, or even virtual movements of avatars in online games have also been used as proxies for human movements.

These studies have provided valuable insights into several aspects of human mobility, uncovering distinct features of human travel behavior such as scaling laws or predictability of trajectories among others. Besides empirical studies, the surge of available data on human mobility has also evoked interest in developing new theoretical models of mobility at several scales. Such models have deep implications for various subjects ranging from epidemiology to urbanism, with special importance in city planning and policy action.

Being movement an activity based on a displacement between two points, it can naturally be studied from the point of view of networks. This research line of our lab focuses on developping theoretical and techincal tools to allow the study of human mobility processes taking a statistical phyisics view.

Learn more about it in: CEPS (Collective Emergent Phenomena in Physical Systems)

Multiplex Networks

Albert Diaz-Guilera, M. Ángeles Serrano and Marián Boguñá

The Science of Complex Systems is an emergent discipline rather successful in the last years. However, further progress in the physics is hampered by the lack of deep knowledge about how multi-level complex systems organize and operate. Preliminary results show that interactions at different levels behave in a significantly different way than in an isolated level. For example, such dependencies may induce cascading failures and sudden collapses of the entire system. This makes the science of complex networks particularly suitable for the exploration of the many challenges that we face today, including critical infrastructures and communication systems, as well as techno-social and socioeconomic networks.

We have been working in the development of a mathematical, computational and algorithmic framework for the study of the physics of multiscale complex systems. The chosen framework consists in a set of layers in such a way that every single layer has exactly the same set of nodes, but they can have different patterns of connectivity. A clear example can be that of social networks, where a layer can be a set of Twitter users having its respective set of following and followed users and another layer can be the same set of Facebook users. A user can have different sets of neighbours in each network because one can think on more familiar or more professional links. But the set of users is exactly the same. In this case, one can imagine that information can flow in any of the two layers and dhifting from one to the other when one of the users decide to do it.

Learn more about it in: CEPS (Collective Emergent Phenomena in Physical Systems)
and in: Mapping Complexity Lab

Network Geometry

M. Ángeles Serrano and Marián Boguñá

Geometry appears as the most plausible explanation of the complex architecture we observe in real networks. Scale-free degree distributions, clustering, small-world property, communities, reciprocity and many more topological properties can be explained by the existence of a metric space controlling the network interactions.

Learn more about it in: Mapping Complexity Lab

Networks in Cosmology

Marián Boguñá

The causal structure of spacetime and standard cosmological models can be easily mapped into hyperbolic geometry. Quite interestingly, networks that arise in this context are extremely similar to networks we find in domains as diverse as cell biology, social sciences, or socio-technological systems, like the Internet or the world wide web.

Learn more about it in: Mapping Complexity Lab

Socio-technologic Systems

Marián Boguñá

In the age of Information Technology, the Internet has become our primary communication system. It is estimated that more than a billion users surf every day the web looking for information, sharing files, or developing new applications. The physical Internet is like a new world where all kind of new social and technological structures are constantly emerging. The Internet has thus become a common good, such as roads, railways, or airline connections and, as such, should be considered. The most surprising fact about the Internet is that, despite some preconceived ideas, its complex architecture is the result of a self-organized process where individual agents (Internet Service Providers or ISPs) interact locally without any central authority controlling its evolution. This turns the Internet into subject of truly scientific research.

Our main motivation for studying the Internet comes from long-standing scalability problems with the Internet routing architecture. To route information packets to a given destination, Internet routers must communicate to maintain a coherent view of the global Internet topology. The constantly increasing size and dynamics of the Internet thus leads to immense and quickly growing communication and information processing overhead, a major bottleneck in routing scalability causing concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade. In our research, we assume that the Internet (and other complex networks) lives in a hidden metric space that shapes its topology. Discovery of this hidden metric space can then be used to greedily route information without detailed global knowledge of the network structure or organization.

Learn more about it in: Mapping Complexity Lab

Production and Distribution of Food during the Roman Empire

Albert Díaz-Guilera

We are currently collaborating with historians, archaeologists, and computer scientists to set up an innovative framework to investigate the political and economic mechanisms that characterized the dynamics of the commercial trade system during the Roman Empire. It is a project funded by the European Research Council and our contribution is to introduce network theory as an appropriate description for some trade realtions during the Roman Empire.

Learn more about it in: CEPS (Collective Emergent Phenomena in Physical Systems)

Stochastic Dynamics and Extreme Time Events for Socio-economic Systems

Josep Perelló

The use of time series analysis and stochastic process modeling in complex systems studies has a long tradition, going back to to the application of Brownian (Gaussian) motion modeling to prices in the Paris stock market by Bachelier in 1900.

These models and the statistics behind are best documented in the study of human activity patterns, and include burstiness, long-range cross-correlation and auto-correlation, and strong non-Gaussanity. We have mostly focussed on those aspects valid for the study of financial markets time series although we also recently also analyzed aspects with crutial interest in the economics of climate change.

During the last decade, the group has focused on a number of major challenges in this area including the alignment between theoretical and empirical analysis of extreme events, data driven probability inference in time-series and direct parameter estimation in agent-based modelling.

We have solved and analyzed a large class of stochastic models. Some of them are defined in terms of a Langevin equation or a stochastic differential equation and, in some cases, we also treat multidimensional and coupled diffusion processes. Another approach we have explored is by means of the so-called Continuous Time Random Walk framework.

Learn more about it in: OpenSystems

Statistical mechanics of non-binary networks

Conrad J. Pérez-Vicente

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization.

Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. Moreover, non-binary adjacency matrices can be constructed in multiple ways such as aggregating multiple layers of information. This "additional" dimension that weights confere to networks makes its study in terms of entropy and randomness an interesting subject. Questions such as: How many (different) network can we build with prescribed properties? Which are the apropriate statistics to model weighted networks? or Can those be uniquely defined? can be then posed.

The way of tackling such problems opens the door to apply many well-known and stablished tools of Classical Statistical mechanics to the study of networks, yet it also offers the possibility to perform a critical review of such tools and to explore the limits of this analogy.

Learn more about it in: CEPS (Collective Emergent Phenomena in Physical Systems)

Information and Rumor Spreading in Online Social Media

Emanuele Cozzo

Our research explores the mechanisms behind the spread of information and rumors on online social media platforms by combining mathematical modeling and large-scale data analysis. We develop and analyze Markovian models to describe how content propagates through user interactions, with particular attention to phase transitions between active and inactive regimes of spreading. These transitions help us understand when and why certain content becomes viral while other content quickly fades. We also investigate localization phenomena, where information remains confined to specific regions of the network rather than spreading broadly, and the emergence of polarization and echo chambers in online environments. By analyzing longitudinal data and simulating opinion dynamics, we aim to understand how algorithmic amplification, homophily, and network structure contribute to ideological segregation.

We calibrate our models using real-world social media datasets to test theoretical predictions and identify the key mechanisms driving these complex social processes.

Learn more about it in: CEPS (Collective Emergent Phenomena in Physical Systems)

Opinion Dynamics and Decision Making

Emanuele Cozzo

We investigate the dynamics of opinion formation by developing mathematical models that remain analytically and computationally tractable while incorporating key mechanisms identified in social psychology. Our goal is to bridge the gap between abstract models and empirical behavioral insights, capturing how individuals influence one another, resist persuasion, or take decisions. We focus particularly on identifying the conditions under which consensus can—or cannot—be reached within a population.

Understanding these mechanisms is crucial for addressing pressing global challenges, such as climate change, where collective agreement is essential for coordinated action in a complex environment. Our research adopts a participatory approach, in which experimental designs are co-developed with relevant stakeholders to ensure contextual relevance and real-world applicability. These controlled experiments serve to refine and calibrate our models, allowing us to test how individuals update their opinions in response to different forms of social influence and information exposure.

Learn more about it in: CEPS (Collective Emergent Phenomena in Physical Systems)