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Edge importance in a network via line graphs and the matrix exponential

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Abstract

This paper is concerned with the identification of important edges in a network, in both their roles as transmitters and receivers of information. We propose a method based on computing the matrix exponential of a matrix associated with a line graph of the given network. Both undirected and directed networks are considered. Edges may be given positive weights. Computed examples illustrate the performance of the proposed method.

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Funding

This research is financially supported in part by NSF grants DMS-1720259 and DMS-1729509.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    Omar De la Cruz Cabrera, Mona Matar & Lothar Reichel

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  1. Omar De la Cruz Cabrera
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  2. Mona Matar
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  3. Lothar Reichel
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Correspondence to Omar De la Cruz Cabrera.

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De la Cruz Cabrera, O., Matar, M. & Reichel, L. Edge importance in a network via line graphs and the matrix exponential. Numer Algor 83, 807–832 (2020). https://doi.org/10.1007/s11075-019-00704-y

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