Correlated multiplexity and connectivity of multiplex random networks

Lee, Kyu Min; Kim, Jung Yeol; Cho, Won Kuk; Goh, K.-I.; Kim, I. M.

doi:10.1088/1367-2630/14/3/033027

Cited by 198 publications

(194 citation statements)

References 27 publications

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“…where the first two terms give the size of the giant unicomponent, S = 1 − G 0 ( u) [12], and the last term gives the difference between S and B.…”

Section: A Generating Function Methodsmentioning

confidence: 99%

“…[12]. In the MP case, node's degrees in differ- ent layers are maximally correlated in their degree order, whereas they are maximally anti-correlated in the MN case.…”

Section: Introductionmentioning

confidence: 98%

“…On the contrary, the hub in one layer would have few neighbors in the other layers for negatively correlated multiplex networks. Recently, the effect of such interlayer degree correlation was addressed for connectivity of multiplex networks [12]. Furthermore, a few studies demonstrated that interdependent networks with higher interlayer degree correlation [23,24] or more assortative layers [25] are more robust under random * kgoh@korea.ac.kr damage.…”

Section: Introductionmentioning

confidence: 99%

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Network robustness of multiplex networks with interlayer degree correlations

et al. 2014

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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 maximallycorrelated 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.

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“…where the first two terms give the size of the giant unicomponent, S = 1 − G 0 ( u) [12], and the last term gives the difference between S and B.…”

Section: A Generating Function Methodsmentioning

confidence: 99%

“…[12]. In the MP case, node's degrees in differ- ent layers are maximally correlated in their degree order, whereas they are maximally anti-correlated in the MN case.…”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Network robustness of multiplex networks with interlayer degree correlations

et al. 2014

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“…While most of the current models have a percolative flavour [10][11][12][13], some new directions in understanding the dynamics on NetONets are being explored [14][15][16] resorting to the spectral properties of networks. The European efforts on the subject have recently concentrated in the ''MULTIPLEX'' project [17] combining top scientists in Complexity and Algorithmic.…”

Section: Prefacementioning

confidence: 99%

Networks of Networks: The Last Frontier of Complexity

D’Agostino¹,

Scala²

2014

Understanding Complex Systems

156

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Complexity is an interdisciplinary program publishing the best research and academic-level teaching on both fundamental and applied aspects of complex systems-cutting across all traditional disciplines of the natural and life sciences, engineering, economics, medicine, neuroscience, social and computer science.Complex Systems are systems that comprise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous formation of distinctive temporal, spatial or functional structures. Models of such systems can be successfully mapped onto quite diverse ''real-life'' situations like the climate, the coherent emission of light from lasers, chemical reaction-diffusion systems, biological cellular networks, the dynamics of stock markets and of the internet, earthquake statistics and prediction, freeway traffic, the human brain, or the formation of opinions in social systems, to name just some of the popular applications.Although their scope and methodologies overlap somewhat, one can distinguish the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, turbulence, dynamical systems, catastrophes, instabilities, stochastic processes, chaos, graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence.The three major book publication platforms of the Springer Complexity program are the monograph series ''Understanding Complex Systems'' focusing on the various applications of complexity, and the ''Springer Series in Synergetics'', which is devoted to the quantitative theoretical and methodological foundations, and the ''SpringerBriefs in Complexity'' which are concise and topical working reports, case-studies, surveys, essays and lecture notes of relevance to the field. In addition to the books in these two core series, the program also incorporates individual titles ranging from textbooks to major reference works.

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“…Recent studies alone this line include empirical analysis of real-world network data [11,12], evolution of network structures [13][14][15], and new critical phenomena and processes occurring on them [9,10,16,17]. These coupled networks exhibit some common features, such as the inter degree-degree correlation [18], inter-similarity [19], multiple dependence in providing support [9], and node and edge overlapping between layers [20]. These features have important effects on critical phenomena and the dynamics, including percolation [9], cascading failure [16], diffusion processes [21], emergence of cooperation [22] and epidemic dynamics [17], when compared with those in a single network.…”

Section: Introductionmentioning

confidence: 99%

Suppressed epidemics in multirelational networks

Wang

Cai

et al. 2015

Phys. Rev. E

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A two-state epidemic model in networks with links mimicking two kinds of relationships between connected nodes is introduced. Links of weights w1 and w0 occur with probabilities p and 1 − p, respectively. The fraction of infected nodes ρ(p) shows a non-monotonic behavior, with ρ drops with p for small p and increases for large p. For small to moderate w1/w0 ratios, ρ(p) exhibits a minimum that signifies an optimal suppression. For large w1/w0 ratios, the suppression leads to an absorbing phase consisting only of healthy nodes within a range pL ≤ p ≤ pR, and an active phase with mixed infected and healthy nodes for p < pL and p > pR. A mean field theory that ignores spatial correlation is shown to give qualitative agreement and capture all the key features. A physical picture that emphasizes the intricate interplay between infections via w0 links and within clusters formed by nodes carrying the w1 links is presented. The absorbing state at large w1/w0 ratios results when the clusters are big enough to disrupt the spread via w0 links and yet small enough to avoid an epidemic within the clusters. A theory that uses the possible local environments of a node as variables is formulated. The theory gives results in good agreement with simulation results, thereby showing the necessity of including longer spatial correlations.

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Correlated multiplexity and connectivity of multiplex random networks

Cited by 198 publications

References 27 publications

Network robustness of multiplex networks with interlayer degree correlations

Network robustness of multiplex networks with interlayer degree correlations

Networks of Networks: The Last Frontier of Complexity

Suppressed epidemics in multirelational networks

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