arXiv subjects

Gergely Palla

Publications and source records attributed to Gergely Palla.

At least 19 recordsLinked to original sources

arXiv2026

Robustness in sparse artificial neural networks trained with adaptive topology

We investigate the robustness of sparse artificial neural networks trained with adaptive topology. We focus on a simple yet effective architecture consisting of three sparse layers with 99% sparsity followed by a dense layer, applied to image classification tasks such as MNIST and Fashion MNIST. By updating the topology of the sparse layers between each epoch, we achieve competitive accuracy despite the significantly reduced number of weights. Our primary contribution is a detailed analysis of the robustness of these networks, exploring their performance under various perturbations including random link removal, adversarial attack, and link weight shuffling. Through extensive experiments, we demonstrate that adaptive topology not only enhances efficiency but also maintains robustness. This work highlights the potential of adaptive sparse networks as a promising direction for developing efficient and reliable deep learning models.

cs.LG↗

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↗

arXiv2025

Hierarchy and ranking in pairwise sports contests

Ranking athletes by their performance in competitions and tournaments is common in every popular sport and has significant benefits that contribute to both the organization and strategic aspects of competitions. Although rankings are perhaps the most concise and most straightforward representation of the relative strength among the competitors, beyond this one-dimensional characterization, it is also possible to capture the relationships between athletes in greater detail. Following this approach, our study examines the networks between athletes in individual sports such as tennis and fencing, where the nodes are associated with the contestants and the edges are directed from the winner to the loser. We demonstrate that the connections formed through matches arrange themselves into a time-evolving hierarchy, with the top players positioned at its apex. The structure of the resulting networks exhibits detectable differences depending on whether they are constructed purely from round-robin data or from purely elimination-style tournaments. We find that elimination tournaments lead to networks with a smaller level of hierarchy and thus, importantly, to an increased probability of circular win-loss situations (cycles). The position within the hierarchy, along with other network metrics, can be used to predict match outcomes. In the systems studied, these methods provide predictions with an accuracy comparable to that of forecasts based on official sports ranking points or the Elo rating system. A deeper understanding of the delicate aspects of the networks of pairwise contests enhances our ability to model, predict, and optimize the behaviour of many complex systems, whether in sports tournaments, social interactions, or other competitive environments.

physics.soc-ph↗

arXiv2025

Community detection in hypergraphs through hyperedge percolation

Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes, hypergraphs become necessary, creating a need for specialised community detection methods. Here, we adapt the classical $k$-clique percolation method to hypergraphs, constructing communities from hyperedges containing at least $k$ nodes, defining hyperedge adjacency similarly to clique adjacency. Although the analogy between the proposed hyperedge percolation method and the classical clique percolation algorithm is evident, we show that communities obtained directly from the hyperedges can differ from those identified via clique percolation on the pairwise projection of the hypergraph. We also propose an alternative way for merging hyperedges into communities, where instead of imposing a lower bound on hyperedge cardinality, we restrict the maximum size of the considered hyperedges. This alternative algorithm better suits hypergraphs where larger hyperedges realise weaker linkages between the nodes. After comparing the suggested two approaches on simple synthetic hypergraphs designed to highlight their distinctions, we test them on hypergraphs generated by a newly proposed geometric process on the hyperbolic plane, as well as on some real-world examples.

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

Opinion polarisation in social networks driven by cognitive dissonance avoidance

As the consequences of opinion polarization effect our everyday life in more and more aspect, the understanding of its origins and driving forces becomes increasingly important. Here we develop an agent-based network model with realistic human traits: individuals in our simulations are endowed with an internal belief system which they attempt to keep as coherent as possible. This desire -- to reassure existing attitudes while avoiding cognitive dissonance -- is one of the most influential and widely accepted theories in social psychology by now. Our model shows that even in networks that start out completely uniform (from a society of clones), this effort leads to fragmentation and polarization, reflected both by the individual beliefs (attitudes) and the emerging communities in the social network. By fine-tuning two parameters: (i) "dissonance penalty", measuring the strength with which agents attempt to avoid cognitive dissonance, and (ii) "triadic closure affinity", the parameter reflecting agents' likelihood to connect with friends of friends, a wide range of possible community structures are observed.

physics.soc-ph↗

arXiv2024

Iterative embedding and reweighting of complex networks reveals community structure

Graph embeddings learn the structure of networks and represent it in low-dimensional vector spaces. Community structure is one of the features that are recognized and reproduced by embeddings. We show that an iterative procedure, in which a graph is repeatedly embedded and its links are reweighted based on the geometric proximity between the nodes, reinforces intra-community links and weakens inter-community links, making the clusters of the initial network more visible and more easily detectable. The geometric separation between the communities can become so strong that even a very simple parsing of the links may recover the communities as isolated components with surprisingly high precision. Furthermore, when used as a pre-processing step, our embedding and reweighting procedure can improve the performance of traditional community detection algorithms.

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↗

arXiv2023

Greedy routing optimisation in hyperbolic networks

Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods take advantage of the exponentially growing volume of the hyperbolic space as a function of the radius from the origin, allowing a (roughly) uniform spatial distribution of the nodes even for scale-free small-world networks, where the connection probability between pairs decays with hyperbolic distance. One of the motivations behind hyperbolic embedding is that optimal placement of the nodes in a hyperbolic space is widely thought to enable efficient navigation on top of the network. According to that, one of the measures that can be used to quantify the quality of different embeddings is given by the fraction of successful greedy paths following a simple navigation protocol based on the hyperbolic coordinates. In the present work, we develop an optimisation scheme for this score in the native disk representation of the hyperbolic space. This optimisation algorithm can be either used as an embedding method alone, or it can be applied to improve this score for embeddings obtained from other methods. According to our tests on synthetic and real networks, the proposed optimisation can considerably enhance the success rate of greedy paths in several cases, improving the given embedding from the point of view of navigability.

physics.soc-ph↗

arXiv2022

Subdiffusive semantic evolution in Indo-European languages

How do words change their meaning? Although semantic evolution is driven by a variety of distinct factors, including linguistic, societal, and technological ones, we find that there is one law that holds universally across five major Indo-European languages: that semantic evolution is strongly subdiffusive. Using an automated pipeline of diachronic distributional semantic embedding that controls for underlying symmetries, we show that words follow stochastic trajectories in meaning space with an anomalous diffusion exponent $α= 0.45\pm 0.05$ across languages, in contrast with diffusing particles that follow $α=1$. Randomization methods indicate that preserving temporal correlations in semantic change directions is necessary to recover strongly subdiffusive behavior; however, correlations in change sizes play an important role too. We furthermore show that strong subdiffusion is a robust phenomenon under a wide variety of choices in data analysis and interpretation, such as the choice of fitting an ensemble average of displacements or averaging best-fit exponents of individual word trajectories.

physics.soc-ph↗

arXiv2022

Model-independent methods for embedding directed networks into Euclidean and hyperbolic spaces

The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods have already been developed for the hyperbolic embedding of undirected networks, approaches able to deal with directed networks are still in their infancy. Here, we propose a framework based on the dimension reduction of proximity matrices reflecting the network topology, coupled with a general conversion method transforming Euclidean node coordinates into hyperbolic ones even for directed networks. While proposing a new measure of proximity, we also incorporate an earlier Euclidean embedding method in our pipeline, demonstrating the widespread applicability of our Euclidean-hyperbolic conversion. Besides, we introduce a dimension reduction technique that maps the nodes directly into the hyperbolic space with the aim of reproducing a distance matrix measured on the given (un)directed network. According to mapping accuracy, graph reconstruction performance and greedy routing score, our methods are capable of producing high-quality embeddings for several real networks.

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↗

arXiv2021

The inherent community structure of hyperbolic networks

A remarkable approach for grasping the relevant statistical features of real networks with the help of random graphs is offered by hyperbolic models, centred around the idea of placing nodes in a low-dimensional hyperbolic space, and connecting node pairs with a probability depending on the hyperbolic distance. It is widely appreciated that these models can generate random graphs that are small-world, highly clustered and scale-free at the same time; thus, reproducing the most fundamental common features of real networks. In the present work, we focus on a less well-known property of the popularity-similarity optimisation (PSO) model and the $\mathbb{S}^1/\mathbb{H}^2$ model from this model family, namely that the networks generated by these approaches also contain communities for a wide range of the parameters, which was certainly not an intention at the design of the models. We extracted the communities from the studied networks using well-established community finding methods such as Louvain, Infomap and label propagation. The observed high modularity values indicate that the community structure can become very pronounced under certain conditions. In addition, the modules found by the different algorithms show good consistency, implying that these are indeed relevant and apparent structural units. Since the appearance of communities is rather common in networks representing real systems as well, this feature of hyperbolic models makes them even more suitable for describing real networks than thought before.

physics.soc-ph↗

arXiv2020

Optimisation of the coalescent hyperbolic embedding of complex networks

Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between the nodes. A remarkable network model generating random graphs along this line is the popularity-similarity optimisation (PSO) model, offering a scale-free degree distribution, high clustering and the small world property at the same time. These results provide a strong motivation for the development of hyperbolic embedding algorithms, that tackle the problem of finding the optimal hyperbolic coordinates of the nodes based on the network structure. A very promising recent approach for hyperbolic embedding is provided by the noncentered minimum curvilinear embedding (ncMCE) method, belonging to the family of coalescent embedding algorithms. This approach offers a high quality embedding at a low running time. In the present work we propose a further optimisation of the angular coordinates in this framework that seems to reduce the logarithmic loss and increase the greedy routing score of the embedding compared to the original version, thereby adding an extra improvement to the quality of the inferred hyperbolic coordinates.

cs.SI↗

arXiv2020

Networks with degree-degree correlations is a special case of edge-coloured random graphs

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent nodes by showing that such networks are a special case of edge-coloured random graphs. We use this mapping to study bond percolation in networks with assortative mixing and show that, unlike in networks with independent degrees, the sizes of connected components may feature unexpected sensitivity to perturbations in the degree distribution. The results also indicate that degree-degree dependencies may feature a vanishing percolation threshold even when the second moment of the degree distribution is finite. These results may be used to design artificial networks that efficiently withstand link failures and indicate possibility of super spreading in networks without clearly distinct hubs

math.CO↗

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

On community structure in complex networks: challenges and opportunities

Community structure is one of the most relevant features encountered in numerous real-world applications of networked systems. Despite the tremendous effort of scientists working on this subject over the past few decades to characterize, model, and analyze communities, more investigations are needed to better understand the impact of community structure and its dynamics on networked systems. Here, we first focus on generative models of communities in complex networks and their role in developing strong foundation for community detection algorithms. We discuss modularity and the use of modularity maximization as the basis for community detection. Then, we overview the Stochastic Block Model, its different variants, and inference of community structures from such models. Next, we focus on time evolving networks, where existing nodes and links can disappear and/or new nodes and links may be introduced. The extraction of communities under such circumstances poses an interesting and non-trivial problem that has gained considerable interest over the last decade. We briefly discuss considerable advances made in this field recently. Finally, we focus on immunization strategies essential for targeting the influential spreaders of epidemics in modular networks. Their main goal is to select and immunize a small proportion of individuals from the whole network to control the diffusion process. Various strategies have emerged over the years suggesting different ways to immunize nodes in networks with overlapping and non-overlapping community structure. We first discuss stochastic strategies that require little or no information about the network topology at the expense of their performance. Then, we introduce deterministic strategies that have proven to be very efficient in controlling the epidemic outbreaks, but require complete knowledge of the network.

physics.soc-ph↗