MariĆ”n BoguĆ±Ć” Espinal
Marián Boguñá Espinal (Barcelona, 1967) is an associate professor at the Departament de Física de la Matèria Condensada of the Universitat de Barcelona. He graduated in Physics in 1994 and obtained his PhD also in Physics in 1998. In 1999, he moved to the USA to do a postdoctoral stay with Professor George H. Weiss at the National Institutes of Health, Washington DC. After this period, he moved back to Barcelona where, in 2003, he was awarded a Ramón y Cajal fellowship. He got the tenure position at the end of 2008. During this period, he has also spent several months in the USA as invited guest scientist at Indiana University. M. Boguñá has written over 70 publications in major peer reviewed international scientific journals, book chapters, and conference proceedings. Among those, Nature, Nature Physics, Nature Communications, Proceedings of the National Academy of Sciences US, Physical Review Letters, and Physical Review X. He was the chair of the international conference BCNetWORKSHOP 2008 Trends and Perspectives in Complex Networks and has served as a program committee member in many international conferences. In January 2008, he obtained the Outstanding Referee award of the American Physical Society. In December 2010 and 2015, he was awarded as ICREA Academia researcher 2010 and 2015, respectively. Since January 2013 he serves as an editorial board member for Scientific Reports.
Absence of Epidemic Threshold in ScaleFree Networks with Degree Correlations
Boguna, M; PastorSatorras, R; Vespignani, A
PHYSICAL REVIEW LETTERS
90
28701
(2003)
Random scalefree networks have the peculiar property of being prone to the spreading of infections. Here we provide for the susceptibleinfectedsusceptible model an exact result showing that a scalefree degree distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or disassortative mixing. Degree correlations result therefore irrelevant for the epidemic spreading picture in these scalefree networks. The present result is related to the divergence of the average nearest neighbor´s degree, enforced by the degree detailed balance condition.
Class of correlated random networks with hidden variables
Boguna, M; PastorSatorras, R
PHYSICAL REVIEW E
68
36112
(2003)
We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.
Hyperbolic geometry of complex networks
Krioukov, D; Papadopoulos, F; Kitsak, M; Vahdat, A; Boguna, M
Physical Review E
82
36106
(2010)
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure.
Navigability of complex networks
Boguna, M; Krioukov, D; Claffy, KC
Nature Physics
5
7480
(2009)
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Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of distributed computation. However, in many real networks, nodes communicate efficiently even without such global intelligence. Here, we show that the peculiar structural characteristics of many complex networks support efficient communication without global knowledge. We also describe a general mechanism that explains this connection between network structure and function. This mechanism relies on the presence of a metric space hidden behind an observable network. Our findings suggest that real networks in nature have underlying metric spaces that remain undiscovered. Their discovery should have practical applications in a wide range of areas where networks are used to model complex systems.
Extracting the multiscale backbone of complex weighted networks
Serrano, MA; Boguna, M; Vespignani, A
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
106
64836488
(2009)
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⇕ suppl. files
A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In recent years, the study of an increasing number of largescale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions that vary over many orders of magnitude. These features, along with the large number of elements and links, make the extraction of the truly relevant connections forming the network´s backbone a very challenging problem. More specifically, coarsegraining approaches and filtering techniques come into conflict with the multiscale nature of largescale systems. Here, we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks, preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges. An important aspect of the method is that it does not belittle smallscale interactions and operates at all scales defined by the weight distribution. We apply our method to realworld network instances and compare the obtained results with alternative backbone extraction techniques.
Popularity versus similarity in growing networks
Fragkiskos Papadopoulos, Maksim Kitsak, M. Ćngeles Serrano, MariĆ”n BoguĆ±Ć”, and Dmitri Krioukov
Nature
489
537540
(2012)
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The principle that ‘popularity is attractive’ underlies preferential attachment, which is a common explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribution of the number of connections possessed by nodes follows power laws, as observed in many real networks. Preferential attachment has been directly validated for some real networks (including the Internet), and can be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks or duplication. Here we show that popularity is just one dimension of attractiveness; another dimension is similarity. We develop a framework in which new connections optimize certain tradeoffs between popularity and similarity, instead of simply preferring popular nodes.The framework has a geometric interpretation in which popularity preference emerges from local optimization. As opposed to preferential attachment, our optimization framework accurately describes the largescale evolution of technological (the Internet), social (trust relationships between people) and biological (Escherichia coli metabolic) networks, predicting the probability of new links with high precision.The framework that we have developed can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon.
Sustaining the Internet with hyperbolic mapping
BoguĆ±Ć”, M; Papadopoulos, F; Krioukov, D
Nature Communications
1
62
(2010)
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The Internet infrastructure is severely stressed. Rapidly growing overheads associated with the primary function of the Internet—routing information packets between any two computers in the world—cause concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade. In this paper, we present a method to map the Internet to a hyperbolic space. Guided by a constructed map, which we release with this paper, Internet routing exhibits scaling properties that are theoretically close to the best possible, thus resolving serious scaling limitations that the Internet faces today. Besides this immediate practical viability, our network mapping method can provide a different perspective on the community structure in complex networks.
Epidemic spreading on interconnected networks
Anna SaumellMendiola, M. Ćngeles Serrano, and MariĆ”n BoguĆ±Ć”
Physical Review E
86
026106
(2012)
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⇕ media coverage
Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop a heterogeneous mean field approach that allows us to calculate the conditions for the emergence of an endemic state. Interestingly, a global endemic state may arise in the coupled system even though the epidemics is not able to propagate on each network separately, and even when the number of coupling connections is small. Our analytic results are successfully confronted against largescale numerical simulations.
Selfsimilarity of complex networks and hidden metric spaces
Serrano, MA; Krioukov, D; Boguna, M
PHYSICAL REVIEW LETTERS
100
78701
(2008)
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⇕ suppl. files
We demonstrate that the selfsimilarity of some scalefree networks with respect to a simple degreethresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the selfsimilarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their selfsimilarity with respect to the degreebased renormalization.
Percolation and Epidemic Thresholds in Clustered Networks
Serrano, MA; Boguna, M
PHYSICAL REVIEW LETTERS
97
88701
(2006)
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scalefree networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks, thus extending this result to a wide variety of real scalefree networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.
Nature of the Epidemic Threshold for the SusceptibleInfectedSusceptible Dynamics in Networks
MariĆ”n BoguĆ±Ć”, Claudio Castellano, and Romualdo PastorSatorras
Physical Review Letters
111
068701
(2013)
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⇕ suppl. files
We develop an analytical approach to the susceptibleinfectedsusceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, smallworld random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.
Network Cosmology
Dmitri Krioukov, Maksim Kitsak, Robert S. Sinkovits, David Rideout, David Meyer, MariĆ”n BoguĆ±Ć”
Scientific Reports
2
793
(2012)
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⇕ suppl. files
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Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the largescale structure of spacetime in our accelerating universe is a powerlaw graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the largescale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology.
Navigating Ultrasmall Worlds in Ultrashort Time
Boguna, M; Krioukov, D
PHYSICAL REVIEW LETTERS
102
58701
(2009)
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⇕ media coverage
Random scalefree networks are ultrasmall worlds. The average length of the shortest paths in networks of size N scales as lnlnN. Here we show that these ultrasmall worlds can be navigated in ultrashort time. Greedy routing on scalefree networks embedded in metric spaces finds paths with the average length scaling also as lnlnN. Greedy routing uses only local information to navigate a network. Nevertheless, it finds asymptotically the shortest paths, a direct computation of which requires global topology knowledge. Our findings imply that the peculiar structure of complex networks ensures that the lack of global topological awareness has asymptotically no impact on the length of communication paths. These results have important consequences for communication systems such as the Internet, where maintaining knowledge of current topology is a major scalability bottleneck.
Double percolation phase transition in clustered complex networks
Pol ColomerdeSimĆ³n and MariĆ”n BoguĆ±Ć”
Physical Review X
4
041020
(2014)
The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to smallworld and scalefree properties, clustering is the most common topological characteristic observed in many real networked systems. In this paper, we report an extensive numerical study on the effects of clustering on the structural properties of complex networks. Strong clustering in heterogeneous networks induces the emergence of a coreperiphery organization that has a critical effect on the percolation properties of the networks. We observe a novel double phase transition with an intermediate phase in which only the core of the network is percolated and a final phase in which the periphery percolates regardless of the core. This result implies breaking of the same symmetry at two different values of the control parameter, in stark contrast to the modern theory of continuous phase transitions. Inspired by this coreperiphery organization, we introduce a simple model that allows us to analytically prove that such an anomalous phase transition is in fact possible.
Percolation in selfsimilar networks
M. Ćngeles Serrano, Dmitri Krioukov, and MariĆ”n Boguna
Physical Review Letters
106
048701
(2011)
We provide a simple proof that graphs in a general class of selfsimilar networks have zero percolation threshold. The considered selfsimilar networks include random scalefree graphs with given expected node degrees and zero clustering, scalefree graphs with finite clustering and metric structure, growing scalefree networks, and many real networks. The proof and the derivation of the giant component size do not require the assumption that networks are treelike. Our results rely only on the observation that selfsimilar networks possess a hierarchy of nested subgraphs whose average degree grows with their depth in the hierarchy. We conjecture that this property is pivotal for percolation in networks.
Hidden geometric correlations in real multiplex networks
KajKolja Kleineberg, MariĆ”n BoguĆ±Ć”, M. Ćngeles Serrano, and Fragkiskos Papadopoulos
Nature Physics
12
1076 1081
(2016)
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Real networks often form interacting parts of larger and more complex systems. Examples can be found in di erent domains, ranging from the Internet to structural and functional brain networks. Here, we show that these 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. We find that these correlations are significant in di erent real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate translayer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow e cient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are su ciently strong.
The geometric nature of weights in real complex networks
Antoine Allard, M. Ćngeles Serrano, Guillermo GarcĆaPĆ©rez, and MariĆ”n BoguĆ±Ć”
Nature Communications
8
14103
(2017)
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The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet’s routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich character ization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.
Geometric correlations mitigate the extreme vulnerability of multiplex networks against targeted attacks
KajKolja Kleineberg, Lubos Buzna, Fragkiskos Papadopoulos, MariĆ”n BoguĆ±Ć”, and M. Ćngeles Serrano
Physical Review Letters
118
218301
(2017)
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⇕ suppl. files
We show that real multiplex networks are unexpectedly robust against targeted attacks on highdegree nodes and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.

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