arXiv subjects

Sang Hoon Lee

Publications and source records attributed to Sang Hoon Lee.

At least 19 recordsLinked to original sources

arXiv2026

Ecological networks of viable species with degree-dependent interaction

The generalized Lotka-Volterra (GLV) framework, recently advanced by dynamical mean-field theory, enables the systematic analysis of large ecological networks. When combined with structured interaction topologies, previous studies have shown that the viability of species, defined by having a positive stationary abundance, depends on the number of their interacting neighbors or the "degree." While such model studies usually assume that interaction strengths follow an identical distribution across all connected pairs, real ecological communities often exhibit correlations between interaction strength and a species' degree. To capture this overlooked feature, we introduce degree-dependent interaction strengths into a generalized random LV model. We identify two distinct regimes: a hub-favored phase, where highly connected species survive preferentially, and a hub-suppressed phase, where they face higher extinction risks. We analytically derive the phase boundary where these degree-dependent strengths precisely balance the connectivity effect, leaving all species equally susceptible. Crucially, these phases induce opposing shifts in the degree-degree correlation or "assortativity" of the network of viable species: the hub-favored phase enhances disassortativity by selectively removing the interactions between low-degree species, whereas the hub-suppressed phase reduces it as the interactions involving hub species tend to disappear. Ultimately, our findings demonstrate that degree-dependent interactions are a fundamental mechanism not only for shaping species survival, but for naturally reproducing the wide range of assortativity values observed in real ecological networks.

q-bio.PE↗

arXiv2026

Evaluating the impact of incomplete contact tracing data on urban epidemic dynamics

Contact tracing (CT) is a frontline measure against emerging epidemics, yet in practice it is never complete. The quantitative impact of missing information -- such as untraced cases or unnotified contacts -- on the effectiveness of CT remains insufficiently understood. Using a stochastic agent-based model with sociodemographics from metropolitan areas in South Korea, we simulate how different forms of information loss affect epidemic spreading dynamics. We construct information-loss scenarios based on two types: infector-omission (IO), the omission of infected individuals from the tracing process, and contact-omission (CO), the omission of specific contact events even when the infected individuals themselves are identified. The sensitivity of epidemic dynamics to increasing omission rates differs markedly between the two types: IO produces substantially stronger and more abrupt changes in transmission structure and epidemic outcomes, whereas CO produces more gradual effects. Notably, CT effectiveness breaks down beyond a city-specific threshold -- an IO rate of approximately 4% in Seoul but about 10% in less populous Busan -- underscoring that CT strategies must be tailored to regional population and mobility structure. Both IO and CO scenarios also lead to an increase in the transmission network diameter as information loss grows, indicating that a small network diameter reflects effective contact tracing that limits the depth of transmission chains. Collectively, our results offer threshold estimates and practical guidance for designing robust CT systems in the real world.

physics.soc-ph↗

arXiv2025

Friendship-paradox paradox: Do most people's friends really have more friends than they do?

The classical friendship paradox asserts that, on average, an individual's neighbors have a higher degree than the individual. This statement concerns network-level means and does not describe how often a typical node is locally dominated by its neighbors. Motivated by this distinction, we develop a framework that separates mean-based friendship paradox inequalities from two majority-type quantities: a global fraction measuring how many nodes have a degree smaller than the mean degree of their neighbors, and a local fraction based on hub centrality that measures how many nodes are dominated in a median-based sense. We show that neither fraction is constrained by the classical friendship paradox and that they can behave independently of each other. A simple example and two empirical networks illustrate how quadrant patterns in the joint distribution of a node's degree and its neighbors' degree determine the signs and magnitudes of the two fractions, and how left- or right-skewed degree distributions of neighboring nodes can yield opposite conclusions for mean-based and median-based comparisons. The resulting framework offers a clearer distinction between population averages and local majority relations and provides a foundation for future analyses of local advantage, disadvantage, and perception asymmetry in complex networks.

physics.soc-ph↗

arXiv2025

Two variants of the friendship paradox: The condition for inequality between them

The friendship paradox -- the observation that, on average, one's friends have more friends than oneself -- admits two common formulations depending on whether averaging is performed over edges or over nodes. These two definitions, the "alter-based" and "ego-based" means, are often treated as distinct but related quantities. This paper establishes their exact analytical relationship, showing that the difference between them is governed by the degree-degree covariance normalized by the mean degree. Explicit examples demonstrate the three possible cases of positive, zero, and negative covariance, corresponding respectively to assortative, neutral, and disassortative mixing patterns. The derivation further connects the covariance form to the moment-based expression introduced by Kumar, Krackhardt, and Feld [Proc. Natl. Acad. Sci. 121, e2306412121 (2024)], which involves the (-1)st, 1st, 2nd, and 3rd moments of the degree distribution. The two formulations are shown to be equivalent, as they should be: the moment-based representation expands the same structural dependence that the covariance form expresses in its most compact and interpretable form. The analysis thus unifies node-level and moment-level perspectives on the friendship paradox, offering both a pedagogically transparent derivation and a direct bridge to recent theoretical developments.

physics.soc-ph↗

arXiv2025

Effects of relational graph modularity and depth on the learning performance of neural networks

In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph structure of neural networks and their predictive performance, they often limit themselves to a narrow range of model networks, particularly lacking mesoscale structures such as communities. Our work advances this area by conducting a more comprehensive investigation, incorporating realistic network structures characterized by heterogeneous degree distributions and community structures, which are typical characteristics of many real networks. These community structures offer a nuanced perspective on network architecture. Our analysis employs model networks such as random and scale-free networks, alongside a comparison with a biological neural network and its subsets for more detailed analysis. We examine the impact of these structural attributes on the performance of image classification tasks. Our findings reveal that structural properties do affect performance to some extent. Specifically, within moderate-depth architectures, networks featuring coherent, densely interconnected communities demonstrate enhanced learning capabilities. Crucially, we find that this advantage is strictly depth-dependent: extending the architecture to eight layers reverses the effect entirely. This comparison with the biological neural network emphasizes the relevance of our findings to real-world structures, suggesting an intriguing connection worth further exploration. This study contributes meaningfully to network science and machine learning, providing insights that could inspire the design of more biologically informed neural networks.

cs.LG↗

arXiv2025

Quantifying interdisciplinary synergy in higher STEM education

We propose a framework to quantify and utilize interdisciplinarity in science and engineering curricula at the university-level higher education. We analyze interdisciplinary relations by standardizing large-scale official educational data in Korea using a cutting-edge large language model and constructing knowledge maps for disciplines of scientific education. We design and evaluate single-field and integrated dual-field curricula by adapting pedagogical theory and utilizing information theory-based metrics. We develop standard curricula for individual disciplines and integrated curricula combining two fields, with their interdisciplinarity quantified by the curriculum synergy score. The results indicate higher interdisciplinarity for combinations within or across closely related fields, especially in engineering fields. Based on the analysis, engineering fields constitute the core structure of our design for curriculum interdisciplinarity, while basic natural science fields are located at peripheral stems to provide fundamental concepts.

physics.soc-ph↗

arXiv2024

Kaleidoscopic reorganization of network communities across different scales

The notion of structural heterogeneity is pervasive in real networks, and their community organization is no exception. Still, a vast majority of community detection methods assume neatly hierarchically organized communities of a characteristic scale for a given hierarchical level. In this work, we demonstrate that the reality of scale-dependent community reorganization is convoluted with simultaneous processes of community splitting and merging, challenging the conventional understanding of community-scale adjustment. We provide a mathematical argument concerning the modularity function, the results from real-network analysis, and a simple network model for a comprehensive understanding of the nontrivial community reorganization process. The reorganization is characterized by a local drop in the number of communities as the resolution parameter varies. This study suggests a need for a paradigm shift in the study of network communities, which emphasizes the importance of considering scale-dependent reorganization to better understand the genuine structural organization of networks.

physics.soc-ph↗

arXiv2024

Global decomposition of networks into multiple cores formed by local hubs

Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking inside, using the concept of locally defined nodal hub centrality and edge-pruning techniques built upon it. We demonstrate that the hub-centrality-based edge pruning reveals a series of breaking points in network decomposition, which effectively separates a network into its backbone and shell structures. Our local-edge decomposition method iteratively identifies and removes locally least connected nodes, and uncovers an onion-like hierarchical structure as a result. Compared with the conventional $k$-core decomposition method, our method based on relative information residing in local structures exhibits a clear advantage in terms of discovering locally crucial substructures. As an application of the method, we present a scheme to detect multiple core-periphery structures and the decomposition of coarse-grained supernode networks, by combining the method with the network community detection.

physics.soc-ph↗

arXiv2024

Statistical Analysis on Scale and Regional Distribution of Undergraduate Physics Programs in Korean Universities

We report on the temporal changes in undergraduate-level physics programs at Korean universities from 1915 to 2023 by analyzing data on physics-related departments and their students using basic statistics and the scaling theory of statistical physics. Our analysis reveals that the number of departments peaked around the turn of the 21st century, and it has been steadily decreasing ever since, with particularly severe declines in private universities located outside the capital region. Besides the change in the overall numbers, we also show the change in the self-identity of physics-related departments reflected in department names, which reveals a recent trend of emphasizing more application-side such as semiconductors and data. As a sophisticated measure to quantify regional imbalances relative to the population eligible for higher education, we present scaling exponents from the scaling theory, which shows a shift from sublinear to linear for departments and a shift from linear to superlinear for students. The result indicates the exacerbation of the regional imbalance of university-level physics education in Korea.

physics.ed-ph↗

arXiv2024

Incorporating Heterogeneous Interactions for Ecological Biodiversity

Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical mean-field theory to provide insights into underlying principles such as how biodiversity and stability depend on the randomness in interaction strength. Yet the fully-connected structure assumed in these previous studies is not realistic as revealed by a vast amount of empirical data. We derive a generic formula for the abundance distribution under an arbitrary distribution of degree, the number of interacting neighbors, which leads to degree-dependent abundance patterns of species. Notably, in contrast to the well-mixed system, the number of surviving species can be reduced as the community becomes cooperative in heterogeneous interaction structures. Our study, therefore, demonstrates that properly taking into account heterogeneity in the interspecific interaction structure is indispensable to understanding the diversity in large ecosystems, and our general theoretical framework can apply to a much wider range of interacting many-body systems.

physics.bio-ph↗

arXiv2024

Renormalization of Complex Networks with Partition Functions

While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than resorting to handling the bare structure of a network, we overlay it with a readily renormalizable physical model, which reflects real-world scenarios with a broad generality. From the renormalization of the overlying system, we extract a rigorous and simple renormalization group transformation of arbitrary networks. In this way, we obtain a transparent, model-dependent physical meaning of the network renormalization, which in our case is a scale transformation preserving the transition dynamics of low-density particles. We define the strength of a node in accordance with the physical model and trace the change of its distribution under our renormalization process. This analysis demonstrates that the strength distributions of scale-free networks remain scale-invariant, whereas those of homogeneous random networks do not.

cond-mat.stat-mech↗

arXiv2023

Revisiting small-world network models: Exploring technical realizations and the equivalence of the Newman-Watts and Harary models

We address the relatively less known facts on the equivalence and technical realizations surrounding two network models showing the "small-world" property, namely the Newman-Watts and the Harary models. We provide the most accurate (in terms of faithfulness to the original literature) versions of these models to clarify the deviation from them existing in their variants adopted in one of the most popular network analysis packages. The difference in technical realizations of those models could be conceived as minor details, but we discover significantly notable changes caused by the possibly inadvertent modification. For the Harary model, the stochasticity in the original formulation allows a much wider range of the clustering coefficient and the average shortest path length. For the Newman-Watts model, due to the drastically different degree distributions, the clustering coefficient can also be affected, which is verified by our higher-order analytic derivation. During the process, we discover the equivalence of the Newman-Watts (better known in the network science or physics community) and the Harary (better known in the graph theory or mathematics community) models under a specific condition of restricted parity in variables, which would bridge the two relatively independently developed models in different fields. Our result highlights the importance of each detailed step in constructing network models and the possibility of deeply related models, even if they might initially appear distinct in terms of the time period or the academic disciplines from which they emerged.

physics.soc-ph↗

arXiv2023

Exploring 3D community inconsistency in human chromosome contact networks

Researchers developed chromosome capture methods such as Hi-C to better understand DNA's 3D folding in nuclei. The Hi-C method captures contact frequencies between DNA segment pairs across the genome. When analyzing Hi-C data sets, it is common to group these pairs using standard bioinformatics methods (e.g., PCA). Other approaches handle Hi-C data as weighted networks, where connected node represent DNA segments in 3D proximity. In this representation, one can leverage community detection techniques developed in complex network theory to group nodes into mesoscale communities containing similar connection patterns. While there are several successful attempts to analyze Hi-C data in this way, it is common to report and study the most typical community structure. But in reality, there are often several valid candidates. Therefore, depending on algorithm design, different community detection methods focusing on slightly different connectivity features may have differing views on the ideal node groupings. In fact, even the same community detection method may yield different results if using a stochastic algorithm. This ambiguity is fundamental to community detection and shared by most complex networks whenever interactions span all scales in the network. This is known as community inconsistency. This paper explores this inconsistency of 3D communities in Hi-C data for all human chromosomes. We base our analysis on two inconsistency metrics, one local and one global, and quantify the network scales where the community separation is most variable. For example, we find that TADs are less reliable than A/B compartments and that nodes with highly variable node-community memberships are associated with open chromatin. Overall, our study provides a helpful framework for data-driven researchers and increases awareness of some inherent challenges when clustering Hi-C data into 3D communities.

physics.soc-ph↗

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↗

arXiv2021

Refinement for community structures of bipartite networks

Bipartite networks composed of dichotomous node sets are ubiquitous in nature and society. Partly for simplicity's sake, many studies have focused on their projection onto their unipartite versions where one only needs to care about a single type of node. When it comes to mesoscale structures such as communities, however, properly incorporating a priori structural restrictions such as bipartivity is ever more important. In this paper, as a case study, we take the community structure of bipartite networks in various scales to examine the amount of information of bipartivity encoded in the community detection procedure. In particular, we report the robustness in reliability of detected community based on consistency by comparing the detection algorithm with or without the consideration of bipartivity. From the analysis with model networks embedding prescribed communities and real networks, we find that the community detection tailored to take the bipartivity into account clearly yields more robust community structures than the one without such structural information. This demonstrates the necessity for customizing the community detection algorithm by encoding whatever information is known about networks of interest and, at the same time, raises an interesting question on the possibility of estimating the quantitative amount of information from such a customization.

physics.soc-ph↗

arXiv2021

Mesoscale properties of mutualistic networks in ecosystems

Uncovering structural properties of ecological networks is a crucial starting point of studying the system's stability in response to various types of perturbations. We analyze pollination and seed disposal networks, which are representative examples of mutualistic networks in ecosystems, in various scales. In particular, we examine mesoscale properties such as the nested structure, the core-periphery structure, and the community structure by statistically investigating their interrelationships with real network data. As a result of community detection in different scales, we find the absence of meaningful hierarchy between networks, and the negative correlation between the modularity and the two other structures (nestedness and core-periphery-ness), which themselves are highly positively correlated. In addition, no characteristic scale of communities is perceivable from the community-inconsistency analysis. Therefore, the community structures, which are most widely studied mesoscale structures of networks, are not in fact adequate to characterize the mutualistic networks of this scale in ecosystems.

physics.soc-ph↗

arXiv2021

Consistency landscape of network communities

The concept of community detection has long been used as a key device for handling the mesoscale structures in networks. Suitably conducted community detection reveals various embedded informative substructures of network topology. However, regarding the practical usage of community detection, it has always been a tricky problem to assign a reasonable community resolution for networks of interest. Because of the absence of the unanimously accepted criterion, most of the previous studies utilized rather ad hoc heuristics to decide the community resolution. In this work, we harness the concept of consistency in community structures of networks to provide the overall community resolution landscape of networks, which we eventually take to quantify the reliability of detected communities for a given resolution parameter. More precisely, we exploit the ambiguity in the results of stochastic detection algorithms and suggest a method that denotes the relative validity of community structures in regard to their stability of global and local inconsistency measures using multiple detection processes. Applying our framework to synthetic and real networks, we confirm that it effectively displays insightful fundamental aspects of community structures.

physics.soc-ph↗

arXiv2020

Polynomial embeddings of unilateral weighted shifts into $2$-variable weighted shifts

Given a bounded sequence \omega of positive numbers and its associated unilateral weighted shift W_{\omega} acting on the Hilbert space \ell^2(\mathbb{Z}_+), we consider natural representations of W_{\omega} as a 2-variable weighted shift, acting on \ell^2(\mathbb{Z}_+^2). Alternatively, we seek to examine the various ways in which the sequence \omega can give rise to a 2-variable weight diagram. Our best (and more general) embedding arises from looking at two polynomials p and q nonnegative on a closed interval I in R_+ and the double-indexed moment sequence \{\int p(r)^k q(r)^{\ell} d\sigma(r)\}_{k,\ell \in \mathbb{Z}_+}, where W_{\omega} is assumed to be subnormal with Berger measure \sigma such that \supp \; \sigma \subseteq I; we call such an embedding a (p,q)-embedding of W_{\omega}. We prove that every (p,q)-embedding of a subnormal weighted shift W_{\omega} is (jointly) subnormal, and we explicitly compute its Berger measure. We apply this result to answer three outstanding questions: (i) Can the Bergman shift A_2 be embedded in a subnormal 2-variable spherically isometric weighted shift W_{(\alpha,\beta)}? If so, what is the Berger measure of W_{(\alpha,\beta)}? (ii) Can a contractive subnormal unilateral weighted shift be always embedded in a spherically isometric 2-variable weighted shift? (iii) Does there exist a hyponormal 2-variable weighted shift \Theta(W_{\omega}) (where \Theta(W_{\omega}) denotes the classical embedding of a hyponormal unilateral weighted shift W_{\omega}) such that some integer power of \Theta(W_{\omega}) is not hyponormal? As another application, we find an alternative way to compute the Berger measure of the Agler j-th shift A_{j} (j\geq 2). Our research uses techniques from the theory of disintegration of measures, Riesz functionals, and the functional calculus for the columns of the moment matrix associated to a polynomial embedding.

math.FA↗