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Locating multiple diffusion sources in time varying networks from sparse observations.

Zhao-Long Hu1, Zhesi Shen2, Shinan Cao3

  • 1College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China.

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Identifying multiple diffusion sources in dynamic networks is challenging. This study introduces a framework using high-degree "messenger" nodes for accurate source localization, even in rapidly changing networks.

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Area of Science:

  • Network Science
  • Complex Systems
  • Information Theory

Background:

  • Source localization in complex networks is crucial for applications like epidemiology and social network analysis.
  • Locating multiple diffusion sources in time-varying networks remains a significant challenge.
  • Existing methods often struggle with dynamic network structures and limited observational data.

Purpose of the Study:

  • To develop a general framework for identifying multiple diffusion sources in time-varying networks using sparse data.
  • To leverage structural observability and sparse signal reconstruction for robust source localization.
  • To investigate the role of messenger node selection in improving localization accuracy.

Main Methods:

  • Developed a framework integrating structural observability and sparse signal reconstruction theories.
  • Utilized sparse data from a selected subset of messenger nodes within the network.
  • Analyzed network dynamics and node properties (e.g., degree) to optimize messenger selection.

Main Results:

  • Identified high-degree nodes as more informative messengers compared to low-degree nodes in dynamic networks.
  • Demonstrated that sparse observations from a few high-degree nodes are sufficient for locating multiple diffusion sources.
  • Found that more rapidly varying networks can be localized more easily with fewer messengers.

Conclusions:

  • The proposed framework effectively locates multiple diffusion sources in time-varying networks using minimal data.
  • Strategic selection of high-degree nodes as messengers significantly enhances localization performance.
  • Network dynamics influence the efficiency of source localization, with faster changes potentially aiding identification.