arXiv subjects

Kwang-Il Goh

Publications and source records attributed to Kwang-Il Goh.

10 recordsLinked to original sources

arXiv2026

An Approximate-Master-Equation Formulation of the Watts Threshold Model on Hypergraphs

In traditional models of behavioral or opinion dynamics on social networks, researchers suppose that all interactions occur between pairs of individuals. However, in reality, social interactions also occur in groups of three or more individuals. A common way to incorporate such polyadic interactions is to study dynamical processes on hypergraphs. In a hypergraph, interactions can occur between any number of the individuals in a network. The Watts threshold model (WTM) is a well-known model of a simplistic social spreading process. Very recently, Chen et al. extended the WTM from dyadic networks (i.e., graphs) to polyadic networks (i.e., hypergraphs). In the present paper, we extend their discrete-time model to continuous time using approximate master equations (AMEs). By using AMEs, we are able to model the system with very high accuracy. We then reduce the high-dimensional AME system to a system of three coupled differential equations without any detectable loss of accuracy. This much lower-dimensional system is more computationally efficient to solve numerically and is also easier to interpret. We linearize the reduced AME system and calculate a cascade condition, which allows us to determine when a large spreading event occurs. We then apply our model to a social contact network of a French primary school and to a hypergraph of computer-science coauthorships. We find that the AME system is accurate in modelling the polyadic WTM on these empirical networks; however, we expect that future work that incorporates structural correlations between nearby nodes and groups into the model for the dynamics will lead to more accurate theory for real-world networks.

physics.soc-ph↗

arXiv2024

Phase Transitions in the Simplicial Ising Model on Hypergraphs

We study the phase transitions in the simplicial Ising model on hypergraphs, in which the energy within each hyperedge (group) is lowered only when all the member spins are unanimously aligned. The Hamiltonian of the model is equivalent to a weighted sum of lower-order interactions, evoking an Ising model defined on a simplicial complex. Using the Landau free energy approach within the mean-field theory, we identify diverse phase transitions depending on the sizes of hyperedges. Specifically, when all hyperedges have the same size $q$, the nature of the transitions shifts from continuous to discontinuous at the tricritical point $q=4$, with the transition temperatures varying nonmonotonically, revealing the ambivalent effects of group size $q$. Furthermore, if both pairwise edges and hyperedges of size $q>2$ coexist in a hypergraph, novel scenarios emerge, including mixed-order and double transitions, particularly for $q>8$. Adopting the Bethe--Peierls method, we investigate the interplay between pairwise and higher-order interactions in achieving global magnetization, illuminating the multiscale nature of the higher-order dynamics.

cond-mat.stat-mech↗

arXiv2023

Contagion dynamics on hypergraphs with nested hyperedges

In complex social systems encoded as hypergraphs, higher-order (i.e., group) interactions taking place among more than two individuals are represented by hyperedges. One of the higher-order correlation structures native to hypergraphs is the nestedness: Some hyperedges can be entirely contained (that is, nested) within another larger hyperedge, which itself can also be nested further in a hierarchical manner. Yet the effect of such hierarchical structure of hyperedges on the dynamics has remained unexplored. In this context, here we propose a random nested-hypergraph model with a tunable level of nestedness and investigate the effects of nestedness on a higher-order susceptible-infected-susceptible process. By developing an analytic framework called the facet approximation, we obtain the steady-state fraction of infected nodes on the random nested-hypergraph model more accurately than existing methods. Our results show that the hyperedge-nestedness affects the phase diagram significantly. Monte Carlo simulations support the analytical results.

physics.soc-ph↗

arXiv2023

Growing Hypergraphs with Preferential Linking

A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the preferential-attachment models of scale-free networks. We obtain the degree distribution and hyperedge size distribution for various combinations of node- and hyperedge-based growth modes. We find that the introduction of hyperedge-based growth can give rise to power-law degree distribution $P(k)\sim k^{-γ}$ even without node-wise preferential-attachments. The hyperedge size distribution $P(s)$ can take diverse functional forms, ranging from exponential to power-law to a nonstationary one, depending on the specific hyperedge-based growth rule. Numerical simulations support the mean-field theoretical analytical predictions.

physics.soc-ph↗

arXiv2023

$(k,q)$-core decomposition of hypergraphs

In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential subgroups in hypergraphs, named $(k,q)$-core decomposition. The $(k,q)$-core is defined as the maximal subgraph in which each vertex has at least $k$ hypergraph degrees \textit{and} each hyperedge contains at least $q$ vertices. The method contains a repeated pruning process until reaching the $(k,q)$-core, which shares similarities with a widely used $k$-core decomposition technique in a graph. Second, we analyze the pruning dynamics and the percolation transition with theoretical and numerical methods in random hypergraphs. We set up evolution equations for the pruning process, and self-consistency equations for the percolation properties. Based on our theory, we find that the pruning process generates a hybrid percolation transition for either $k\ge 3$ \textit{or} $q\ge 3$. The critical exponents obtained theoretically are confirmed with finite-size scaling analysis. Next, when $k=q=2$, we obtain a unconventional degree-dependent critical relaxation dynamics analytically and numerically. Finally, we apply the $(k,q)$-core decomposition to a real coauthorship dataset and recognize the leading groups at an early stage.

cond-mat.stat-mech↗

arXiv2022

Degree distributions under general node removal: Power-law or Poisson?

Perturbations made to networked systems may result in partial structural loss, such as a blackout in a power-grid system. Investigating the resultant disturbance in network properties is quintessential to understand real networks in action. The removal of nodes is a representative disturbance, but previous studies are seemingly contrasting about its effect on arguably the most fundamental network statistic, the degree distribution. The key question is about the functional form of the degree distributions that can be altered during node removal or sampling, which is decisive in the remaining subnetwork's static and dynamical properties. In this work, we clarify the situation by utilizing the relative entropies with respect to the reference distributions in the Poisson and power-law form. Introducing general sequential node removal processes with continuously different levels of hub protection to encompass a series of scenarios including random removal and preferred or protective removal of the hub, we classify the altered degree distributions starting from various power-law forms by comparing two relative entropy values. From the extensive investigation in various scenarios based on direct node-removal simulations and by solving the rate equation of degree distributions, we discover in the parameter space two distinct regimes, one where the degree distribution is closer to the power-law reference distribution and the other closer to the Poisson distribution.

physics.soc-ph↗

arXiv2016

Strength of weak layers in cascading failures on multiplex networks: case of the international trade network

Many real-world complex systems across natural, social, and economical domains consist of manifold layers to form multiplex networks. The multiple network layers give rise to nonlinear effect for the emergent dynamics of systems. Especially, weak layers that can potentially play significant role in amplifying the vulnerability of multiplex networks might be shadowed in the aggregated single-layer network framework which indiscriminately accumulates all layers. Here we present a simple model of cascading failure on multiplex networks of weight-heterogeneous layers. By simulating the model on the multiplex network of international trades, we found that the multiplex model produces more catastrophic cascading failures which are the result of emergent collective effect of coupling layers, rather than the simple sum thereof. Therefore risks can be systematically underestimated in single-layer network analyses because the impact of weak layers can be overlooked. We anticipate that our simple theoretical study can contribute to further investigation and design of optimal risk-averse real-world complex systems.

physics.soc-ph↗

arXiv2015

Towards real-world complexity: an introduction to multiplex networks

Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the system's structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed.

physics.soc-ph↗

arXiv2011

Impact of the topology of global macroeconomic network on the spreading of economic crises

Throughout economic history, the global economy has experienced recurring crises. The persistent recurrence of such economic crises calls for an understanding of their generic features rather than treating them as singular events. The global economic system is a highly complex system and can best be viewed in terms of a network of interacting macroeconomic agents. In this regard, from the perspective of collective network dynamics, here we explore how the topology of global macroeconomic network affects the patterns of spreading of economic crises. Using a simple toy model of crisis spreading, we demonstrate that an individual country's role in crisis spreading is not only dependent on its gross macroeconomic capacities, but also on its local and global connectivity profile in the context of the world economic network. We find that on one hand clustering of weak links at the regional scale can significantly aggravate the spread of crises, but on the other hand the current network structure at the global scale harbors a higher tolerance of extreme crises compared to more "globalized" random networks. These results suggest that there can be a potential hidden cost in the ongoing globalization movement towards establishing less-constrained, trans-regional economic links between countries, by increasing the vulnerability of global economic system to extreme crises.

q-fin.ST↗

arXiv2006

Burstiness and Memory in Complex Systems

The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intensive activity followed by long times of no or reduced activity. The understanding of the origin of such bursty patterns is hindered by the lack of tools to compare different systems using a common framework. We introduce two measures to distinguish the mechanisms responsible for the bursty nature of real signals, changes in the interevent times and memory. We find that while the burstiness of natural phenomena is rooted in both the interevent time distribution and memory, for human dynamics memory is weak, and the bursty character is due to changes in the interevent time distribution. Finally, we show that current models lack in their ability to reproduce the activity pattern observed in real systems, opening up new avenues for future work.

physics.data-an↗