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Identifying influential nodes based on new layer metrics and layer weighting in multiplex networks

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Abstract

Identifying influential nodes in multiplex complex networks have a critical importance to implement in viral marketing and other real-world information diffusion applications. However, selecting suitable influential spreaders in multiplex networks are more complex due to existing multiple layers. Each layer of multiplex networks has its particular importance. Based on this research, an important layer with strong spreaders is a layer positioned in a well-connected neighborhood with more active edges, active critical nodes, the ratio of active nodes and their connections to all possible connections, and the intersection of intralayer communication compared to other layers. In this paper, we have formulated a layer weighting method based on mentioned layer’s parameters and proposed an algorithm for mapping and computing the rank of nodes based on their spreading capability in multiplex networks. Thus, the result of layer weighting is used in mapping and compressing centrality vector values to a scalar value for calculating the centrality of nodes in multiplex networks by a coupled set of equations. In addition, based on this new method, the important layer parameters are combined for the first time to utilize in computing the influence of nodes from different layers. Experimental results on both synthetic and real-world networks show that the proposed layer weighting and mapping method significantly is effective in detecting high influential spreaders against compared methods. These results validate the specific attention to suitable layer weighting measure for identifying potential spreaders in multiplex network.

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Abbreviations

AE:

Active edges

\({v}_{i_{\phantom{A}}}\) :

Node i

\({k}_{i}^{[\alpha ]}\) :

The degree of node i in layer α

UICL:

Uniqueness of Intralayer communication compared to other layer

\(L\) :

Number of network layers

AE[α] :

Active edges of the layer \(\alpha \)

\(\mathrm{NUICL}\) :

Normalized UICL

ANCPC:

Active nodes and their connections on all potential connections

N :

Denotes the total count of nodes

ANAUIC:

Active node connectivity to all unique interlayer connections

b[α]:

Represent the quantities of active edges and active nodes specifically in the α layer

LCA:

Layer coreness alignment

\({\rm MKC}_{i}\) :

The maximum K-core of layer i

LIV:

Layer influence value

\({\mathrm{SRV}}_{{v}_{i}}\) :

The singular rank value for node \({v}_{i}\)

\({\rm CV}_{{v}_{i}}\) :

The centrality value of individual nodes

SIR:

Susceptible (S) neighbors, infected (I) individuals, recovered (R) individuals

β :

The rate at which susceptible nodes become infected by their already infected neighbors

γ :

The recovery rate of infected nodes

\({\rm SIR}_{{v}_{i}}^{k}\) :

Number of infected nodes by node vi in layer k

\({D}_{R}\) :

Difference between SIR and proposed SRV method

\({R}_{{V}_{i}}^{{\rm SIR}^{\phantom{A}}}\) :

The Rank of node \({V}_{i}\) in top 15 best nodes in SIR list

\({R}_{{V}_{i}}^{{\rm Cl}^{\phantom{A}}}\) :

The gained rank for node \({V}_{i}\) by the centrality measure

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Authors and Affiliations

  1. Department of Computer Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran

    Asgarali Bouyer

  2. Department of Software Engineering, Faculty of Engineering and Natural Science, Istinye University, Istanbul, Turkey

    Asgarali Bouyer & Bahman Arasteh

  3. Department of Computer Engineering and Information Technology,, Payame Noor University, Tehran, Iran

    Moslem Mohammadi

Authors
  1. Asgarali Bouyer
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  2. Moslem Mohammadi
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Contributions

Asgarali Bouyer was contributed to idea definition and conceptualization, methodology, method evaluation, interpretation of results, review and editing. Moslem Mohammadi Jenghara was contributed to programming, idea definition, experimental results and comparison Bahman Arasteh was contributed to methodology, editing.

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Correspondence to Asgarali Bouyer.

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Bouyer, A., Mohammadi, M. & Arasteh, B. Identifying influential nodes based on new layer metrics and layer weighting in multiplex networks. Knowl Inf Syst 66, 1011–1035 (2024). https://doi.org/10.1007/s10115-023-01983-7

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