arXiv subjects

M. Angeles Serrano

Publications and source records attributed to M. Angeles Serrano.

At least 19 recordsLinked to original sources

arXiv2021

Detecting the ultra low dimensionality of real networks

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 networks from 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.

physics.soc-ph↗

arXiv2020

Network Geometry

Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry 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 all 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 utility in a variety of practical applications, ranging from the understanding how the brain works, to routing in the Internet. Here, we review the most important theoretical and practical developments dealing with these approaches to network geometry in the last two decades, and offer perspectives on future research directions and challenges in this novel frontier in the study of complexity.

physics.soc-ph↗

arXiv2019

Small worlds and clustering in spatial networks

Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current surge of activity in graph embedding. In the vast realm of spatial network models, only a few reproduce even the most basic properties of real-world networks. Here, we focus on three such properties--sparsity, small worldness, and clustering--and identify the general subclass of spatial homogeneous and heterogeneous network models that are sparse small worlds and that have nonzero clustering in the thermodynamic limit. We rely on the maximum entropy approach where network links correspond to noninteracting fermions whose energy dependence on spatial distances determines network small worldness and clustering.

physics.soc-ph↗

arXiv2017

Hidden geometric correlations in real multiplex networks

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different 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 individual layers. We find that these correlations are strong in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate: (i) the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers; (ii) accurate trans-layer link prediction, where connections in one layer can be predicted by observing the hidden geometric space of another layer; and (iii) efficient targeted navigation in the multilayer system using only local knowledge, which outperforms navigation in the single layers only if the geometric correlations are sufficiently strong. Our findings uncover fundamental organizing principles behind real multiplexes and can have important applications in diverse domains.

physics.soc-ph↗

arXiv2015

Escaping the avalanche collapse in self-similar multiplexes

We deduce and discuss the implications of self-similarity for the stability in terms of robustness to failure of multiplexes, depending on interlayer degree correlations. First, we define self-similarity of multiplexes and we illustrate the concept in practice using the configuration model ensemble. Circumscribing robustness to survival of the mutually percolated state, we find a new explanation based on self-similarity both for the observed fragility of interconnected systems of networks and for their robustness to failure when interlayer degree correlations are present. Extending the self-similarity arguments, we show that interlayer degree correlations can change completely the stability properties of self-similar multiplexes, so that they can even recover a zero percolation threshold and a continuous transition in the thermodynamic limit, qualitatively exhibiting thus the ordinary stability attributes of noninteracting networks. We confirm these results with numerical simulations.

physics.soc-ph↗

arXiv2014

Simulating non-Markovian stochastic processes

We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the Gillespie algorithm for Markovian processes, with the difference that now the occurrence rates of the events depend on the time elapsed since the event last took place. We use our non-Markovian generalized Gillespie stochastic simulation methodology to investigate the effects of non-exponential inter-event time distributions in the susceptible-infected-susceptible model of epidemic spreading. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction. We also assess our generalized Gillespie algorithm on a system of biochemical reactions with time delays. As compared to other existing methods, we find that the generalized Gillespie algorithm is the most general as it can be implemented very easily in cases, like for delays coupled to the evolution of the system, where other algorithms do not work or need adapted versions, less efficient in computational terms.

cond-mat.dis-nn↗

arXiv2014

The complex architecture of primes and natural numbers

Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cramér's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cramér's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help to get deeper insights about primes and the complex architecture of natural numbers.

math.NT↗

arXiv2013

Deciphering the global organization of clustering in real complex networks

We uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered with respect to clustering, although they tend to be closer to maximally random architectures. We reach this conclusion by comparing the global structure of clustering in real networks with that in maximally random and in maximally ordered clustered graphs. The former are produced with an exponential random graph model that maintains correlations among adjacent edges at the minimum needed to conform with the expected clustering spectrum; the later with a random model that arranges triangles in cliques inducing highly ordered structures. To compare the global organization of clustering in real and model networks, we compute $m$-core landscapes, where the $m$-core is defined, akin to the $k$-core, as the maximal subgraph with edges participating at least in $m$ triangles. This property defines a set of nested subgraphs that, contrarily to $k$-cores, is able to distinguish between hierarchical and modular architectures. To visualize the $m$-core decomposition we developed the LaNet-vi 3.0 tool.

physics.soc-ph↗

arXiv2013

Popularity versus Similarity in Growing Networks

Popularity is attractive -- this is the formula underlying preferential attachment, a popular 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 that nodes have follows power laws observed in many real networks. Preferential attachment has been directly validated for some real networks, including the Internet. Preferential attachment can also 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 where new connections, instead of preferring popular nodes, optimize certain trade-offs between popularity and similarity. The framework admits a geometric interpretation, in which popularity preference emerges from local optimization. As opposed to preferential attachment, the optimization framework accurately describes large-scale evolution of technological (Internet), social (web of trust), and biological (E.coli metabolic) networks, predicting the probability of new links in them with a remarkable precision. The developed framework can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon.

physics.soc-ph↗

arXiv2012

A measure of individual role in collective dynamics

Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several levels: how to single out the role of individual elements in such intermingled systems, or which is the best way to quantify their importance. Centrality measures describe a node's importance by its position in a network. The key issue obviated is that the contribution of a node to the collective behavior is not uniquely determined by the structure of the system but it is a result of the interplay between dynamics and network structure. We show that dynamical influence measures explicitly how strongly a node's dynamical state affects collective behavior. For critical spreading, dynamical influence targets nodes according to their spreading capabilities. For diffusive processes it quantifies how efficiently real systems may be controlled by manipulating a single node.

physics.soc-ph↗

arXiv2011

Uncovering the hidden geometry behind metabolic networks

Metabolism is a fascinating cell machinery underlying life and disease and genome-scale reconstructions provide us with a captivating view of its complexity. However, deciphering the relationship between metabolic structure and function remains a major challenge. In particular, turning observed structural regularities into organizing principles underlying systemic functions is a crucial task that can be significantly addressed after endowing complex network representations of metabolism with the notion of geometric distance. Here, we design a cartographic map of metabolic networks by embedding them into a simple geometry that provides a natural explanation for their observed network topology and that codifies node proximity as a measure of hidden structural similarities. We assume a simple and general connectivity law that gives more probability of interaction to metabolite/reaction pairs which are closer in the hidden space. Remarkably, we find an astonishing congruency between the architecture of E. coli and human cell metabolisms and the underlying geometry. In addition, the formalism unveils a backbone-like structure of connected biochemical pathways on the basis of a quantitative cross-talk. Pathways thus acquire a new perspective which challenges their classical view as self-contained functional units.

q-bio.MN↗

arXiv2011

Percolation in self-similar networks

We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering, scale-free graphs with finite clustering and metric structure, growing scale-free 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 self-similar 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.

cond-mat.dis-nn↗

arXiv2009

Extracting the multiscale backbone of complex weighted networks

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 large scale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions which 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, coarse-graining approaches and filtering techniques are at struggle with the multiscale nature of large scale 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 statistical 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 small-scale interactions and operates at all scales defined by the weight distribution. We apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques.

physics.soc-ph↗

arXiv2009

Conservation laws for voter-like models on directed networks

We study the voter model, under node and link update, and the related invasion process on a single strongly connected component of a directed network. We implement an analytical treatment in the thermodynamic limit using the heterogeneous mean field assumption. From the dynamical rules at the microscopic level, we find the equations for the evolution of the relative densities of nodes in a given state on heterogeneous networks with arbitrary degree distribution and degree-degree correlations. We prove that conserved quantities as weighted linear superpositions of spin states exist for all three processes and, for uncorrelated directed networks, we derive their specific expressions. We also discuss the time evolution of the relative densities that decay exponentially to a homogeneous stationary value given by the conserved quantity. The conservation laws obtained in the thermodynamic limit for a system that does not order in that limit determine the probabilities of reaching the absorbing state for a finite system. The contribution of each degree class to the conserved quantity is determined by a local property. Depending on the dynamics, the highest contribution is associated to influential nodes reaching a large number of outgoing neighbors, not too influenceable ones with a low number of incoming connections, or both at the same time.

cond-mat.dis-nn↗

arXiv2009

Beyond Zipf's law: Modeling the structure of human language

Human language, the most powerful communication system in history, is closely associated with cognition. Written text is one of the fundamental manifestations of language, and the study of its universal regularities can give clues about how our brains process information and how we, as a society, organize and share it. Still, only classical patterns such as Zipf's law have been explored in depth. In contrast, other basic properties like the existence of bursts of rare words in specific documents, the topical organization of collections, or the sublinear growth of vocabulary size with the length of a document, have only been studied one by one and mainly applying heuristic methodologies rather than basic principles and general mechanisms. As a consequence, there is a lack of understanding of linguistic processes as complex emergent phenomena. Beyond Zipf's law for word frequencies, here we focus on Heaps' law, burstiness, and the topicality of document collections, which encode correlations within and across documents absent in random null models. We introduce and validate a generative model that explains the simultaneous emergence of all these patterns from simple rules. As a result, we find a connection between the bursty nature of rare words and the topical organization of texts and identify dynamic word ranking and memory across documents as key mechanisms explaining the non trivial organization of written text. Our research can have broad implications and practical applications in computer science, cognitive science, and linguistics.

cs.CL↗

arXiv2008

On Cycles in AS Relationships

Several users of our AS relationship inference data (http://www.caida.org/data/active/as-relationships/), released with cs/0604017, asked us why it contained AS relationship cycles, e.g., cases where AS A is a provider of AS B, B is a provider of C, and C is a provider of A, or other cycle types. Having been answering these questions in private communications, we have eventually decided to write down our answers here for future reference.

cs.NI↗

arXiv2008

Rich-club vs rich-multipolarization phenomena in weighted networks

Large scale hierarchies characterize complex networks in different domains. Elements at their top, usually the most central or influential, may show multipolarization or tend to club forming tightly interconnected communities. The rich-club phenomenon quantified this tendency based on unweighted network representations. Here, we define this metric for weighted networks and discuss the appropriate normalization which preserves nodes' strengths and discounts structural strength-strength correlations if present. We find that in some real networks the results given by the weighted rich-club coefficient can be in sharp contrast to the ones in the unweighted approach. We also discuss that the scanning of the weighted subgraphs formed by the high-strength hubs is able to unveil features contrary to the average: the formation of local alliances in rich-multipolarized environments, or a lack of cohesion even in the presence of rich-club ordering. Beyond structure, this analysis matters for understanding correctly functionalities and dynamical processes relying on hub interconnectedness.

cond-mat.dis-nn↗

arXiv2008

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding 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 self-similarity 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 self-similarity with respect to the degree-based renormalization.

cond-mat.dis-nn↗