Kyu-Min Lee

Multiplexity-facilitated cascades in networks.

Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [Watts, Proc. Natl. Acad. Sci. USA 99, 5766 (2002)] to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active. We show that both combining layers (i.e., realizing other interactions play a role) and splitting a network into layers (i.e., recognizing distinct kinds of interactions) facilitate cascades. Notably, layers unsusceptible to global cascades can cooperatively achieve them if coupled. On one hand, this suggests fundamental limitations on predicting cascades without full knowledge of a systems multiplexity; on the other hand, it offers feasible means to control cascades by introducing or removing sparse layers in an existing network.

Correlated multiplexity and connectivity of multiplex random networks

Nodes in a complex networked system often engage in more than one type of interactions among them; they form a multiplex network with multiple types of links. In real-world complex systems, a nodes degree for one type of links and that for the other are not randomly distributed but correlated, which we term correlated multiplexity. In this paper, we study a simple model of multiplex random networks and demonstrate that the correlated multiplexity can drastically affect the properties of a giant component in the network. Specifically, when the degrees of a node for different interactions in a duplex Erdős–Renyi network are maximally correlated, the network contains the giant component for any nonzero link density. In contrast, when the degrees of a node are maximally anti-correlated, the emergence of the giant component is significantly delayed, yet the entire network becomes connected into a single component at a finite link density. We also discuss the mixing patterns and the cases with imperfect correlated multiplexity.

Network robustness of multiplex networks with interlayer degree correlations.

We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to address various notions of the network robustness relevant to multiplex networks, such as the resilience of ordinary and mutual connectivity under random or targeted node removals, as well as the biconnectivity. We found that correlated coupling can affect the structural robustness of multiplex networks in diverse fashion. For example, for maximally correlated duplex networks, all pairs of nodes in the giant component are connected via at least two independent paths and network structure is highly resilient to random failure. In contrast, anticorrelated duplex networks are on one hand robust against targeted attack on high-degree nodes, but on the other hand they can be vulnerable to random failure.

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.

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 the global macroeconomic network affects the patterns of spreading of economic crises. Using a simple toy model of crisis spreading, we demonstrate that an individual countrys 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 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 vulnerability of the global economic system to extreme crises.

Threshold cascades with response heterogeneity in multiplex networks.

Threshold cascade models have been used to describe the spread of behavior in social networks and cascades of default in financial networks. In some cases, these networks may have multiple kinds of interactions, such as distinct types of social ties or distinct types of financial liabilities; furthermore, nodes may respond in different ways to influence from their neighbors of multiple types. To start to capture such settings in a stylized way, we generalize a threshold cascade model to a multiplex network in which nodes follow one of two response rules: some nodes activate when, in at least one layer, a large enough fraction of neighbors is active, while the other nodes activate when, in all layers, a large enough fraction of neighbors is active. Varying the fractions of nodes following either rule facilitates or inhibits cascades. Near the inhibition regime, global cascades appear discontinuously as the network density increases; however, the cascade grows more slowly over time. This behavior suggests a way in which various collective phenomena in the real world could appear abruptly yet slowly.

Link overlap, viability, and mutual percolation in multiplex networks

Abstract Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the system’s structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the effect of the link overlap across layers despite strong empirical evidences for its significance. In this article, we investigate the effect of the link overlap in the viability of multiplex networks, both analytically and numerically. After a short recap of the original multiplex viability study, the distinctive role of overlapping links in viability and mutual connectivity is emphasized and exploited for setting up a proper analytic framework. A rich phase diagram for viability is obtained and greatly diversified patterns of hysteretic behavior in viability are observed in the presence of link overlap. Mutual percolation with link overlap is revisited as a limit of multiplex viability problem, and the controversy between existing results is clarified. The distinctive role of overlapping links is further demonstrated by the different responses of networks under random removals of overlapping and non-overlapping links, respectively, as well as under several link-removal strategies. Our results show that the link overlap facilitates the viability and mutual percolation; at the same time, the presence of link overlap poses a challenge in analytical approaches to the problem.

Sandpiles on multiplex networks

We introduce the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche dynamics; the system is critical with an asymptotic power-law avalanche size distribution with an exponent τ = 3/2 on duplex random networks. The detailed cascade dynamics, however, is affected by the multiplex coupling. For example, higher-degree nodes such as hubs in scale-free networks fail more often in the multiplex dynamics than in the simplex network counterpart in which different types of edges are simply aggregated. Our results suggest that multiplex modeling would be necessary in order to gain a better understanding of cascading failure phenomena of real-world multiplex complex systems, such as the global economic crisis.

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.

Differential relationship between waist circumference and mortality according to age, sex, and body mass index in Koreans with age of 30–90 years; a nationwide health insurance database study

BackgroundA recent concept is that obesity, assessed by body mass index (BMI), is not always a sign of poor health. Thus, in order to use obesity metrics in clinical decision making, it is important to clarify the relationship between waist circumference (WC), a proxy for abdominal obesity, and mortality.MethodsData were used from 8,796,759 subjects aged between 30 and 90 years, who had participated in the Korea National Health Screening Examination between January 1, 2009 and December 31, 2009 and survived at least 1 year post screening. Data from a mean follow-up time of an additional 5.3 years (time at risk) were analyzed for the relationship between WC and mortality according to age, sex, and BMI category.ResultsAn increased WC of more than 90 cm in men and 85 cm in women showed a definite negative influence on mortality. However, the detailed relationship between WC and mortality was J-shaped or U-shaped according to age, sex, and BMI category. In the normal BMI group, the optimal WC range with the lowest mortality was < 70 cm in men and 70–75 cm in women, whereas in obese individuals a WC between 80 and 90 cm in men and 75 and 85 cm in women showed the lowest mortality. The association between increased WC and higher mortality tended to be more obvious in normal-weight women than in normal-weight men or obese women. Furthermore, in normal-weight and obese women, the effect of increased WC on mortality was more critical for subjects aged < 60 years rather than those aged ≥ 60 years.ConclusionsAbdominal obesity, as measured by WC, showed a significant negative association on mortality, and its association with mortality was different according to age, sex, and BMI category. Therefore, WC should be considered in the assessment of obesity-related health risks, and individualized cut-off points for the definition of a healthy WC according to age, sex, and BMI category are necessary.