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J. Ignacio Alvarez-Hamelin

Publications and source records attributed to J. Ignacio Alvarez-Hamelin.

12 recordsLinked to original sources
arXiv2026

Extremal properties and bounds for the generalized algebraic connectivity of graphs in Euclidean spaces

This article presents new contributions to the study of graph rigidity and its interplay with fundamental graph invariants. Recently, a quantitative measure of graph rigidity in $\mathbb{R}^d$, termed the generalized algebraic connectivity, was introduced. This development extends the notion of algebraic connectivity---the second-smallest eigenvalue of the Laplacian matrix---which is commonly used to quantify graph connectivity. In this work, we show that the generalized algebraic connectivity is bounded above by the algebraic connectivity. To capture this relationship, we introduce the $d$-rigidity ratio, a normalized metric of a graph's rigidity relative to its connectivity. We also investigate the relationship between rigidity and the diameter---a measure of the graph's overall extent. In this context, we provide the maximal diameter achievable by rigid graphs and show that generalized path graphs serve as extremal examples. Moreover, we establish a new upper bound for the algebraic connectivity that depends inversely on the diameter and the vertex connectivity, improving upon previous bounds. Finally, we derive an upper bound for the algebraic connectivity of generalized path graphs that asymptotically improves existing ones by a factor of four.

math.CO↗
arXiv2025

Subframework-based Bearing Rigidity Maintenance Control in Multirobot Networks

This work presents a novel approach for \textit{bearing rigidity} analysis and control in multi-robot networks with sensing constraints and dynamic topology. By decomposing the system's framework into \textit{subframeworks}, we express bearing rigidity -- a global property -- as a set of \textit{local} properties, with rigidity eigenvalues serving as natural \textit{local rigidity measures}. We propose a decentralized gradient-based controller to execute mission-specific commands using only bearing measurements. The controller preserves bearing rigidity by keeping the rigidity eigenvalues above a threshold, using only information exchanged within subframeworks. Simulations evaluate the scheme's effectiveness, underscoring its scalability and practicality.

cs.RO↗
arXiv2025

Synchronization between media followers and political supporters during an election process: towards a real time study

We present an analysis of the dynamics of discussions in Twitter (before it became X) among supporters of various candidates in the 2022 French presidential election, and followers of different types of media. Our study demonstrates that we can automatically detect the synchronization of interest among different groups around specific topics at particular times. We introduce two complementary methods for constructing dynamic semantic networks, each with its own advantages. The growing aggregated network helps identify the reactivation of past topics, while the rolling window network is more sensitive to emerging discussions that, despite their significance, may appear suddenly and have a short lifespan. These two approaches offer distinct perspectives on the discussion landscape. Rather than choosing between them, we advocate for using both, as their comparison provides valuable insights at a relatively low computational and storage cost. Our findings confirm and quantify, on a larger scale and in an automatic, agnostic manner, observations previously made using more qualitative methods. We believed this work represents a step forward in developing methodologies to assess equity in information treatment, an obligation imposed by law on broadcasters that use broadcast spectrum frequencies in certain countries.

cs.SI↗
arXiv2022

Subframework-Based Rigidity Control in Multirobot Networks

This paper presents an alternative approach to the study of distance rigidity in networks of mobile agents, based on a subframework scheme. The advantage of the proposed strategy lies in expressing framework rigidity, which is inherently global, as a set of local properties. Also, we show that a framework's normalized rigidity eigenvalue degrades as the graph's diameter increases. Thus, the rigidity eigenvalue associated to each subframework arise naturally as a local rigidity metric. A decentralized subframework-based controller for maintaining rigidity using only range measurements is developed, which is also aimed to minimize the network's communication load. Finally, we show that the information exchange required by the controller is completed in a finite number of iterations, indicating the convenience of the proposed scheme.

eess.SY↗
arXiv2022

Who talks about what? Comparing the information treatment in traditional media with online discussions

We study the dynamics of interactions between a traditional medium, the New York Times journal, and its followers in Twitter, using a massive dataset. It consists of the metadata of the articles published by the journal during the first year of the COVID-19 pandemic, and the posts published in Twitter by a large set of followers of the @nytimes account along with those published by a set of followers of several other media of different kind. The dynamics of discussions held in Twitter by exclusive followers of a medium show a strong dependence on the medium they follow: the followers of @FoxNews show the highest similarity to each other and a strong differentiation of interests with the general group. Our results also reveal the difference in the attention payed to U.S. presidential elections by the journal and by its followers, and show that the topic related to the ``Black Lives Matter'' movement started in Twitter, and was addressed later by the journal.

physics.soc-ph↗
arXiv2020

Evolution of the political opinion landscape during electoral periods

We present a study of the evolution of the political landscape during the 2015 and 2019 presidential elections in Argentina, based on the data obtained from the micro-blogging platform Twitter. We build a semantic network based on the hashtags used by all the users following at least one of the main candidates. With this network we can detect the topics that are discussed in the society. At a difference with most studies of opinion on social media, we do not choose the topics a priori, they naturally emerge from the community structure of the semantic network instead. We assign to each user a dynamical topic vector which measures the evolution of her/his opinion in this space and allows us to monitor the similarities and differences among groups of supporters of different candidates. Our results show that the method is able to detect the dynamics of formation of opinion on different topics and, in particular, it can capture the reshaping of the political opinion landscape which has led to the inversion of result between the two rounds of the 2015 election.

cs.SI↗
arXiv2020

Learning language variations in news corpora through differential embeddings

There is an increasing interest in the NLP community in capturing variations in the usage of language, either through time (i.e., semantic drift), across regions (as dialects or variants) or in different social contexts (i.e., professional or media technolects). Several successful dynamical embeddings have been proposed that can track semantic change through time. Here we show that a model with a central word representation and a slice-dependent contribution can learn word embeddings from different corpora simultaneously. This model is based on a star-like representation of the slices. We apply it to The New York Times and The Guardian newspapers, and we show that it can capture both temporal dynamics in the yearly slices of each corpus, and language variations between US and UK English in a curated multi-source corpus. We provide an extensive evaluation of this methodology.

cs.CL↗
arXiv2016

Socioeconomic correlations and stratification in social-communication networks

The uneven distribution of wealth and individual economic capacities are among the main forces which shape modern societies and arguably bias the emerging social structures. However, the study of correlations between the social network and economic status of individuals is difficult due to the lack of large-scale multimodal data disclosing both the social ties and economic indicators of the same population. Here, we close this gap through the analysis of coupled datasets recording the mobile phone communications and bank transaction history of one million anonymised individuals living in a Latin American country. We show that wealth and debt are unevenly distributed among people in agreement with the Pareto principle; the observed social structure is strongly stratified, with people being better connected to others of their own socioeconomic class rather than to others of different classes; the social network appears with assortative socioeconomic correlations and tightly connected "rich clubs"; and that egos from the same class live closer to each other but commute further if they are wealthier. These results are based on a representative, society-large population, and empirically demonstrate some long-lasting hypotheses on socioeconomic correlations which potentially lay behind social segregation, and induce differences in human mobility.

cs.SI↗
arXiv2015

Router-level community structure of the Internet Autonomous Systems

The Internet is composed of routing devices connected between them and organized into independent administrative entities: the Autonomous Systems. The existence of different types of Autonomous Systems (like large connectivity providers, Internet Service Providers or universities) together with geographical and economical constraints, turns the Internet into a complex modular and hierarchical network. This organization is reflected in many properties of the Internet topology, like its high degree of clustering and its robustness. In this work, we study the modular structure of the Internet router-level graph in order to assess to what extent the Autonomous Systems satisfy some of the known notions of community structure. We show that the modular structure of the Internet is much richer than what can be captured by the current community detection methods, which are severely affected by resolution limits and by the heterogeneity of the Autonomous Systems. Here we overcome this issue by using a multiresolution detection algorithm combined with a small sample of nodes. We also discuss recent work on community structure in the light of our results.

cs.NI↗
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↗
arXiv2012

Obtaining Communities with a Fitness Growth Process

The study of community structure has been a hot topic of research over the last years. But, while successfully applied in several areas, the concept lacks of a general and precise notion. Facts like the hierarchical structure and heterogeneity of complex networks make it difficult to unify the idea of community and its evaluation. The global functional known as modularity is probably the most used technique in this area. Nevertheless, its limits have been deeply studied. Local techniques as the ones by Lancichinetti et al. and Palla et al. arose as an answer to the resolution limit and degeneracies that modularity has. Here we start from the algorithm by Lancichinetti et al. and propose a unique growth process for a fitness function that, while being local, finds a community partition that covers the whole network, updating the scale parameter dynamically. We test the quality of our results by using a set of benchmarks of heterogeneous graphs. We discuss alternative measures for evaluating the community structure and, in the light of them, infer possible explanations for the better performance of local methods compared to global ones in these cases.

physics.soc-ph↗