arXiv subjects

Sámuel G. Balogh

Publications and source records attributed to Sámuel G. Balogh.

10 recordsLinked to original sources

arXiv2026

Non-Pharmaceutical Interventions Reshape Network Immunization Outcomes

Herd immunity is shaped not only by the infection capacity of a spreading epidemic or the contact structure of the hosting population, but also by how and under what circumstances individuals acquire immunity. Immunization strategies may interact with ongoing non-pharmaceutical interventions, which commonly aim to reduce social contact numbers. We demonstrate that these interactions can induce unexpectedly strong and counterintuitive effects on herd immunity. We explore these phenomena on spatially embedded contact networks and uncover a reversal in the relative effectiveness of disease- versus vaccine-induced immunization schemes, highlighting the average number of contacts as a critical determinant of emerging herd immunity. In sparse geometric networks with limited degree heterogeneity, uniform vaccination proves most effective; however, as average contact numbers increase, naturally acquired immunity ultimately becomes the better strategy. We show that this phenomenon may emerge not only in synthetic networks but also in real-world mixing networks, observed during non-pharmaceutical intervention periods across multiple states of the United States.

physics.soc-ph↗

arXiv2026

Network geometry of the Drosophila brain

The recent reconstruction of the Drosophila brain provides a neural network of unprecedented size and level of details. In this work, we study the geometrical properties of this system by applying network embedding techniques to the graph of synaptic connections. Since previous analysis have revealed an inhomogeneous degree distribution, we first employ a hyperbolic embedding approach that maps the neural network onto a point cloud in the two-dimensional hyperbolic space. In general, hyperbolic embedding methods exploit the exponentially growing volume of hyperbolic space with increasing distance from the origin, allowing for an approximately uniform spatial distribution of nodes even in scale-free, small-world networks. By evaluating multiple embedding quality metrics, we find that the network structure is well captured by the resulting two-dimensional hyperbolic embedding, and in fact is more congruent with this representation than with the original neuron coordinates in three-dimensional Euclidean space. In order to examine the network geometry in a broader context, we also apply the well-known Euclidean network embedding approach Node2vec, where the dimension of the embedding space, $d$ can be set arbitrarily. In 3 dimensions, the Euclidean embedding of the network yields lower quality scores compared to the original neuron coordinates. However, as a function of the embedding dimension the scores show an improving tendency, surpassing the level of the 2d hyperbolic embedding roughly at $d=16$, and reaching a maximum around $d=64$. Since network embeddings can serve as valuable inputs for a variety of downstream machine learning tasks, our results offer new perspectives on the structure and representation of this recently revealed and biologically significant neural network.

physics.soc-ph↗

arXiv2026

Geometric Organization and Inference of Shortest Path Nodes in Soft Random Geometric Graphs

The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be solved precisely and in polynomial time. If, however, the network of interest is only partially observable, the shortest path problem is no longer straightforward. Inspired by the shortest path problem in partially observable networks, we investigate the geometric properties of shortest paths in {\it Euclidean} Soft Random Geometric Graphs (SRGGs). We find that shortest paths are aligned along geodesic curves connecting shortest path endpoints. The strength of the shortest path alignment, as quantified by the average distance to geodesic from shortest path nodes and the average path stretch, is higher for larger SRGGs with short-range connections. In addition, we find that the strength of the shortest path alignment is non-monotonic with respect to the average degree of the SRGG. Based on these observations, we establish the conditions under which the alignment of shortest paths may be sufficiently strong to allow the identification of shortest path nodes based on their proximity to geodesic curves. We show that in partially observable networks with uncertain node positions, our geometric approach can outperform network-based shortest-path algorithms. In practical settings, our findings may have applications to navigation, wireless routing, and flow characterization in infrastructure networks.

physics.soc-ph↗

arXiv2024

CLOVE: Travelling Salesman's approach to hyperbolic embeddings of complex networks with communities

The embedding of complex networks into metric spaces has become a research topic of high interest with a wide variety of proposed methods. Low dimensional hyperbolic spaces offer a natural co-domain for embeddings allowing a roughly uniform spatial distribution of the nodes even for scale-free networks and the efficient navigability and estimation of linking probabilities. According to recent results, the communities of a complex network after optimization can be naturally mapped into well-defined angular sectors of the hyperbolic space. Here we introduce CLOVE, an embedding method exploiting this property based on iterative arrangement of the communities in a hierarchical manner, down to individual nodes. A crucial step in the process is finding the optimal angular order of the communities at a given level of the hierarchy, which is solved based on the Travelling Salesman Problem. Since CLOVE outperforms most of the alternative methods regarding different embedding quality measures and is computationally very efficient, it can be very useful in related down-stream machine learning tasks such as AI based pattern recognition.

physics.soc-ph↗

arXiv2024

Intra-community link formation and modularity in ultracold growing hyperbolic networks

Hyperbolic network models, centered around the idea of placing nodes at random in a hyperbolic space and drawing links according to a probability that decreases as a function of the distance, provide a simple, yet also very capable framework for grasping the small-world, scale-free, highly clustered and modular nature of complex systems that are often referred to as real-world networks. In the present work we study the community structure of networks generated by the Popularity Similarity Optimization model (corresponding to one of the fundamental, widely known hyperbolic models) when the temperature parameter (responsible for tuning the clustering coefficient) is set to the limiting value of zero. By focusing on the intra-community link formation we derive analytical expressions for the expected modularity of a partitioning consisting of equally sized angular sectors in the native disk representation of the 2d hyperbolic space. Our formulas improve earlier results to a great extent, being able to estimate the average modularity (measured by numerical simulations) with high precision in a considerably larger range both in terms of the model parameters and also the relative size of the communities with respect to the entire network. These findings enhance our comprehension of how modules form in hyperbolic networks. The existence of these modules is somewhat unexpected, given the absence of explicit community formation steps in the model definition.

physics.soc-ph↗

arXiv2022

Maximally modular structure of growing hyperbolic networks

Hyperbolic models are remarkably good at reproducing the scale-free, highly clustered and small-world properties of networks representing real complex systems in a very simple framework. Here we show that for the popularity-similarity optimization model from this family, the generated networks become also extremely modular in the thermodynamic limit, in spite of lacking any explicit community formation mechanism in the model definition. According to our analytical results supported by numerical simulations, when the system size is increased, the modularity approaches one surprisingly fast.

physics.soc-ph↗

arXiv2021

Growing hyperbolic networks beyond two dimensions: the generalised popularity-similarity optimisation model

Hyperbolic network models have gained considerable attention in recent years, mainly due to their capability of explaining many peculiar features of real-world networks. One of the most widely known models of this type is the popularity-similarity optimisation (PSO) model, working in the native disk representation of the two-dimensional hyperbolic space and generating networks with small-world property, scale-free degree distribution, high clustering and strong community structure at the same time. With the motivation of better understanding hyperbolic random graphs, we hereby introduce the $d$PSO model, a generalisation of the PSO model to any arbitrary integer dimension $d>2$. The analysis of the obtained networks shows that their major structural properties can be affected by the dimension of the underlying hyperbolic space in a non-trivial way. Our extended framework is not only interesting from a theoretical point of view but can also serve as a starting point for the generalisation of already existing two-dimensional hyperbolic embedding techniques.

physics.soc-ph↗

arXiv2020

Generalized entropies, density of states, and non-extensivity

The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the number of variables, making the Boltzmann-Gibbs-Shannon entropy extensive. In systems with strongly interacting variables, or with variables driven by history-dependent dynamics, this is no longer true. Here we show that contrary to the generally held belief, not only strong correlations or history-dependence, but skewed-enough distribution of visiting probabilities, that is, first-order statistics, also play a role in determining the relation between configuration space size and system size, or, equivalently, the extensive form of generalized entropy. We present a macroscopic formalism describing this interplay between first-order statistics, higher-order statistics, and configuration space growth. We demonstrate that knowing any two strongly restricts the possibilities of the third. We believe that this unified macroscopic picture of emergent degrees of freedom constraining mechanisms provides a step towards finding order in the zoo of strongly interacting complex systems.

cond-mat.stat-mech↗

arXiv2019

Time evolution of the hierarchical networks between PubMed MeSH terms

Hierarchical organisation is a prevalent feature of many complex networks appearing in nature and society. A relating interesting, yet less studied question is how does a hierarchical network evolve over time? Here we take a data driven approach and examine the time evolution of the network between the Medical Subject Headings (MeSH) provided by the National Center for Biotechnology Information (NCBI, part of the U. S. National Library of Medicine). The network between the MeSH terms is organised into 16 different, yearly updated hierarchies such as "Anatomy", "Diseases", "Chemicals and Drugs", etc. The natural representation of these hierarchies is given by directed acyclic graphs, composed of links pointing from nodes higher in the hierarchy towards nodes in lower levels. Due to the yearly updates, the structure of these networks is subject to constant evolution: new MeSH terms can appear, terms becoming obsolete can be deleted or be merged with other terms, and also already existing parts of the network may be rewired. We examine various statistical properties of the time evolution, with a special focus on the attachment and detachment mechanisms of the links, and find a few general features that are characteristic for all MeSH hierarchies. According to the results, the hierarchies investigated display an interesting interplay between non-uniform preference with respect to multiple different topological and hierarchical properties.

physics.soc-ph↗

arXiv2019

Generalised thresholding of hidden variable network models with scale-free property

The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most advantageous property - namely proven to be able to reproduce a wide range of different degree distribution forms - it has become a standard tool for generating networks having the scale-free property. One of the most intensively studied version of this model is based on a thresholding mechanism of the exponentially distributed hidden variables associated to the nodes (intrinsic vertex weights), which give rise to the emergence of a scale-free network where the degree distribution $p(k)\sim k^{-γ}$ is decaying with an exponent of $γ=2$. Here we propose a generalization and modification of this model by extending the set of connection probabilities and hidden variable distributions that lead to the aforementioned degree distribution, and analyze the conditions leading to the above behavior analytically. In addition, we propose a relaxation of the hard threshold in the connection probabilities, which opens up the possibility for obtaining sparse scale free networks with arbitrary scaling exponent.

physics.soc-ph↗