arXiv subjects

Felipe Xavier Costa

Publications and source records attributed to Felipe Xavier Costa.

5 recordsLinked to original sources

arXiv2026

Distance Backbones Optimize Spreading Dynamics and Centrality Ranks in the Sparsification of Complex Networks

Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges while preserving desired network properties. Distance backbones of weighted graphs, which remove edges that break a generalized triangle inequality for any given path-length measure, preserve all shortest paths of weighted graphs. They have been shown to typically sparsify graphs more, as well as preserve community structure and spreading dynamics better than alternative state-of-the-art methods. Here, We show that they significantly best preserve node centrality ranks, as well as local and global dynamics in spreading phenomena. This is done by introducing the distance backbone synthesis (DBS) to progressively sparsify weighted graphs according to a general family of nested distance backbones, whereby each edge is associated with the smallest distance backbone in which it appears. DBS provides a principled and natural method to sweep all degrees of sparsification possible while preserving connectivity, allowing us to precisely study (directed and undirected) weighted graph sparsification under multi-objective criteria. It provides an algebraically-principled explanation of edge importance by revealing the precise topological space associated with each edge. The theory is demonstrated with a battery of social contact networks obtained from real-world social activity in different scenarios. Our study also shows that the optimal preservation of node centrality and spreading dynamics happens for the distance backbone obeying the generalized triangle inequality for the path-length measure $g(x, y) = (\sqrt[3]{x}+\sqrt[3]{y})^3$, which removes more than half of the edges from the empirical networks studied.

physics.soc-ph↗

arXiv2025

Quantifying edge relevance for epidemic spreading via the semi-metric topology of complex networks

Sparsification aims at extracting a reduced core of associations that best preserves both the dynamics and topology of networks while reducing the computational cost of simulations. We show that the semi-metric topology of complex networks yields a natural and algebraically-principled sparsification that outperforms existing methods on those goals. Weighted graphs whose edges represent distances between nodes are semi-metric when at least one edge breaks the triangle inequality (transitivity). We first confirm with new experiments that the metric backbone$\unicode{x2013}$a unique subgraph of all edges that obey the triangle inequality and thus preserve all shortest paths$\unicode{x2013}$recovers Susceptible-Infected dynamics over the original non-sparsified graph. This recovery is improved when we remove only those edges that break the triangle inequality significantly, i.e., edges with large semi-metric distortion. Based on these results, we propose the new semi-metric distortion sparsification method to progressively sparsify networks in decreasing order of semi-metric distortion. Our method recovers the macro- and micro-level dynamics of epidemic outbreaks better than other methods while also yielding sparser yet connected subgraphs that preserve all shortest paths. Overall, we show that semi-metric distortion overcomes the limitations of edge betweenness in ranking the dynamical relevance of edges not participating in any shortest path, as it quantifies the existence and strength of alternative transmission pathways.

physics.soc-ph↗

arXiv2022

The distance backbone of directed networks

In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We have previously developed a parameter-free, algebraically-principled methodology to uncover such redundancy and reveal the distance backbone of weighted graphs, which has been shown to be important in transmission dynamics, inference of important paths, and quantifying the robustness of networks. However, the method was developed for undirected graphs. Here we expand this methodology to weighted directed graphs and study the redundancy and robustness found in nine networks ranging from social, biomedical, and technical systems. We found that similarly to undirected graphs, directed graphs in general also contain a large amount of redundancy, as measured by the size of their (directed) distance backbone. Our methodology adds an additional tool to the principled sparsification of complex networks and the measure of their robustness.

cs.SI↗

arXiv2021

Entropic dynamics on Gibbs statistical manifolds

Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here we develop the entropic dynamics of a system the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold which is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an "entropic" notion of time that is tailored to the system under study; the system is its own clock. As one might expect, entropic time is intrinsically directional; there is a natural arrow of time which is lead by entropic considerations. As illustrative examples we discuss dynamics on a space of Gaussians and the discrete 3-state system.

cond-mat.stat-mech↗

arXiv2021

Entropic Dynamics of Networks

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.

physics.soc-ph↗