Networks of networks – An introduction

Kenett, Dror Y.; Perc, Matjaž; Boccaletti, Stefano

doi:10.1016/j.chaos.2015.03.016

Cited by 145 publications

(54 citation statements)

References 61 publications

(74 reference statements)

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“…Becoming aware of this (over)simplification, the scientific community gives increased attention to investigations and development of formalisms regarding temporal [38] and other types of multilayer networks [39][40][41][42][43][44], thereby responding to the fact that several realistic frameworks include multiple subsystems organized as layers of connectivity that can also be dynamic and exhibit multiple types of connections. For example, cells can interact with each other through different signaling mechanisms and hence the corresponding intercellular networks are most firmly presented as a multiplex graph with different layers signifying different pathways.…”

Section: Introductionmentioning

confidence: 99%

Multilayer network representation of membrane potential and cytosolic calcium concentration dynamics in beta cells

Gosak

Dolenšek

Markovič

et al. 2015

Chaos, Solitons & Fractals

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a r t i c l e i n f o a b s t r a c tModern theory of networks has been recognized as a very successful methodological concept for the description and analysis of complex systems. However, some complex systems are more complex than others. For instance, several real-life systems are constituted by interdependent subsystems and their elements are subjected to different types of interactions that can also change with time. Recently, the multilayer network formalism has been proposed as a general theoretical framework for the description and analysis of such multi-dimensional complex systems and is acquiring more and more prominence in terms of a new research direction. In the present study, we use this methodology for the description of functional connectivity patterns and signal propagation between pancreatic beta cells in an islet of Langerhans at the levels of membrane potential (MP) and cytosolic calcium concentration ([Ca 2+ ] c ) dynamics to study the extent of overlap in the two networks and to clarify whether time lags between the two signals in individual cells are in any way dependent on the role these cells play in the functional networks. The two corresponding network layers are constructed on the basis of signal directions and pairwise correlations, whereas the interlayer connections represent the time lag between both measured signals. Our results confirm our previous finding that both MP and [Ca 2+ ] c change spread across an islet in the form of a depolarization and a [Ca 2+ ] c wave, respectively. Both types of waves follow nearly the same path and the networks in both layers have a similar but not entirely the same structure. We show that the observed discrepancies are attributed to variability in delays between the depolarization and rise in [Ca 2+ ] c . In particular, high-degree nodes in both layers are found to exhibit a larger time lag between the MP and the [Ca 2+ ] c signal than nodes with less connections. We speculate that this finding reflects a higher activity of endoplasmic reticulum calcium pumps in the most connected cells. Our findings indicate that visualizing and studying the temporal information flow and interaction patterns between beta cells as a multiplex network can provide valuable new insights into the physiology of the complex signaling processes in islets of Langerhans.

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Section: Introductionmentioning

confidence: 99%

Multilayer network representation of membrane potential and cytosolic calcium concentration dynamics in beta cells

Gosak

Dolenšek

Markovič

et al. 2015

Chaos, Solitons & Fractals

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“…Simple graphs are often used to model relationships between entities in real‐world systems. This approach may, however, be an over‐simplification of a much more complex reality better embraced as several interdependent subsystems (or layers), which motivated the development of the complex networks field [GBSH12, KPB15]. The concept of a multilayer network [KAB*14] builds on and encompasses many existing network definitions across many fields, some of which are much older, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In the area of network visualization, many systems visualize data sets having many characteristics of multilayer networks, albeit under a different title. Multi‐label, multi‐edge, multirelational, multiplex [RMM15, CGGZ*13], heterogeneous [DHRL*12, SKB*14], multimodal [GKL*13, HS09], multiple edge set networks [CMF*14], interdependent networks [GBSH12], interconnected networks [SMSB12] and networks of networks [KPB15] are among the many names given to various types of data that are encapsulated by the multilayer networks definition of Kivelä et al . [KAB*14].…”

Section: Introductionmentioning

confidence: 99%

The State of the Art in Multilayer Network Visualization

McGee

Ghoniem

Mélançon

et al. 2019

Computer Graphics Forum

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Modelling relationship between entities in real‐world systems with a simple graph is a standard approach. However, reality is better embraced as several interdependent subsystems (or layers). Recently, the concept of a multilayer network model has emerged from the field of complex systems. This model can be applied to a wide range of real‐world data sets. Examples of multilayer networks can be found in the domains of life sciences, sociology, digital humanities and more. Within the domain of graph visualization, there are many systems which visualize data sets having many characteristics of multilayer graphs. This report provides a state of the art and a structured analysis of contemporary multilayer network visualization, not only for researchers in visualization, but also for those who aim to visualize multilayer networks in the domain of complex systems, as well as those developing systems across application domains. We have explored the visualization literature to survey visualization techniques suitable for multilayer graph visualization, as well as tools, tasks and analytic techniques from within application domains. This report also identifies the outstanding challenges for multilayer graph visualization and suggests future research directions for addressing them.

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“…Since the pioneering empirical work by Buldyrev et al in 2010 [15], people become to realize that many real networked systems are coupled with other systems, and the interplay between homogenous or heterogeneous systems can display distinct behaviors [16][17][18][19][20][21][22][23][24][25]. As to traffic dynamics on coupled networks, the research is still rare.…”

mentioning

confidence: 99%