An Ensemble Perspective on Multi-layer Networks

Wider, Nicolas; Garas, Antonios; Scholtes, Ingo; Schweitzer, Frank

doi:10.1007/978-3-319-23947-7_3

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…To model dependencies between graphs

G_{p}

and

G_{q}

with their adjacency matrices

A_{p}

and

A_{q}

, a set of cross‐layer adjacency matrices

D_{j}

= (

A_{p, q}, p \neq q

) is obtained. This matrix specifies edges between nodes in different layers, indicating that a multilayer networks G possesses a set of inter‐layer links, connecting nodes across layers (Kivelä et al., 2014; Wider et al., 2016). Research on multilayer networks has permeated numerous fields, encompassing various applications and theoretical aspects such as cross‐layer link prediction (Fan et al., 2019; Jalili et al., 2017), dynamic multilayer network analysis (Jia et al., 2022), and multilayer network embedding (Lu et al., 2018).…”

Section: Related Workmentioning

confidence: 99%

Spatiotemporal analysis of global grain trade multilayer networks considering topological clustering

Tu,

Shu,

et al. 2024

Transactions in GIS

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With accelerating globalization, the complexity of the global grain trade network structure is increasing. Traditional network analysis approaches have certain limitations in capturing these dynamic changes and hidden topological structures in data. Based on global import and export trade data for rice, wheat, and corn from 1988 to 2022, this study has proposed a novel method for the topological clustering of temporal multilayer networks based on topological data analysis in order to systematically assess the topological structure evolution of temporal multilayer networks. The results indicate that different agricultural trade networks reveal hidden clustering characteristics in different years. In addition, this study combines principles from landscape ecology to construct a dynamic community spatiotemporal change model of grain trade networks, aiming to comprehensively reveal potential patterns and dynamic trends in grain trade networks and provide valuable information for grain trade decision‐making.

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“…To model dependencies between graphs

G_{p}

and

G_{q}

with their adjacency matrices

A_{p}

and

A_{q}

, a set of cross‐layer adjacency matrices

D_{j}

= (

A_{p, q}, p \neq q

Section: Related Workmentioning

confidence: 99%

Spatiotemporal analysis of global grain trade multilayer networks considering topological clustering

Tu,

Shu,

et al. 2024

Transactions in GIS

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“…As a result, we obtain a set of cross-layer adjacency matrices Dp = {A l,k , k = l } that specifies the edges between nodes in different layers, where p is the number of dependencies. That is, a multilayer network, G, has a set EI (G) of interlayer links that connect nodes across layers, i.e., for each edge (49,50). The supra-adjacency matrix of the multilayer network G is defined as a block-matrix structure:…”

Section: Multilayer Networkmentioning

confidence: 99%

Topological clustering of multilayer networks

Yuvaraj

Dey

Lyubchich

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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Multilayer networks continue to gain significant attention in many areas of study, particularly due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socioenvironmental ecosystems. However, clustering of multilayer networks, especially using the information on higher-order interactions of the system entities, still remains in its infancy. In turn, higher-order connectivity is often the key in such multilayer network applications as developing optimal partitioning of critical infrastructures in order to isolate unhealthy system components under cyber-physical threats and simultaneous identification of multiple brain regions affected by trauma or mental illness. In this paper, we introduce the concepts of topological data analysis to studies of complex multilayer networks and propose a topological approach for network clustering. The key rationale is to group nodes based not on pairwise connectivity patterns or relationships between observations recorded at two individual nodes but based on how similar in shape their local neighborhoods are at various resolution scales. Since shapes of local node neighborhoods are quantified using a topological summary in terms of persistence diagrams, we refer to the approach as clustering using persistence diagrams (CPD). CPD systematically accounts for the important heterogeneous higher-order properties of node interactions within and in-between network layers and integrates information from the node neighbors. We illustrate the utility of CPD by applying it to an emerging problem of societal importance: vulnerability zoning of residential properties to weather- and climate-induced risks in the context of house insurance claim dynamics.

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“…The multilayer network

scriptG

consists of a total of

\sum_{k = 1}^{m} (||, V ((), G_{k}))

nodes. In addition,

scriptG

has a set

E_{I} ((), G)

of interlayer links which connect nodes across layers, that is, for each edge

((), u, v) \in E_{I} ((), G)

we have u ∈ V ( G k ) and v ∈ V ( G l ) for k ≠ l (Kivelä et al, 2014; Takes et al, 2018; Wider et al, 2016). The adjacency matrix of the multilayer network

scriptG

, which is referred to as supra‐adjacency matrix , can be represented with a block‐matrix structure, where diagonal elements represent within‐layer links and off‐diagonal elements represent cross‐layer links.…”

Section: Community Detection In Multilayer Multiscale and Hypergraph ...mentioning

confidence: 99%

Community detection in complex networks: From statistical foundations to data science applications

Dey

Tian

Gel

2021

WIREs Computational Stats

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Identifying and tracking community structures in complex networks are one of the cornerstones of network studies, spanning multiple disciplines, from statistics to machine learning to social sciences, and involving even a broader range of application areas, from biology to politics to blockchain. This survey paper aims to provide an overview of some most popular approaches in statistical network community detection as well as the newly emerging research directions such as community extraction with higher‐order features and community discovery in multilayer and multiscale networks. Our goal is to offer a unified view at methodological interconnections and the wide spectrum of interdisciplinary data science applications of network community analysis. This article is categorized under: Data: Types and Structure > Graph and Network Data Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification

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An Ensemble Perspective on Multi-layer Networks

Cited by 7 publications

References 18 publications

Spatiotemporal analysis of global grain trade multilayer networks considering topological clustering

Spatiotemporal analysis of global grain trade multilayer networks considering topological clustering

Topological clustering of multilayer networks

Community detection in complex networks: From statistical foundations to data science applications

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