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Modeling Information Diffusion in Online Social Networks with Partial Differential Equations

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  • © 2020

Overview

Authors:
  1. Haiyan Wang

    1. School of Mathematical & Natural Sciences, Arizona State University, Glendale, USA

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  2. Feng Wang

    1. School of Mathematical & Natural Sciences, Arizona State University, Glendale, USA

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  3. Kuai Xu

    1. School of Mathematical & Natural Sciences, Arizona State University, Glendale, USA

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  • Provides a new and timely modeling approach for information diffusion in social media
  • Written by the experts who initiated the approach of modeling with partial differential equations (PDEs)
  • Accessible to a wide range of readers in mathematics, computer science, and social media
  • Presents models which have been validated with real datasets from popular social media sites

Part of the book series: Surveys and Tutorials in the Applied Mathematical Sciences (STAMS, volume 7)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Haiyan Wang, Feng Wang, Kuai Xu
    Pages 1-2

  3. Ordinary Differential Equation Models on Social Networks

    • Haiyan Wang, Feng Wang, Kuai Xu
    Pages 3-13

  4. Spatio-Temporal Patterns of Information Diffusion

    • Haiyan Wang, Feng Wang, Kuai Xu
    Pages 15-25

  5. Clustering of Online Social Network Graphs

    • Haiyan Wang, Feng Wang, Kuai Xu
    Pages 27-41

  6. Partial Differential Equation Models

    • Haiyan Wang, Feng Wang, Kuai Xu
    Pages 43-58

  7. Modeling Complex Interactions

    • Haiyan Wang, Feng Wang, Kuai Xu
    Pages 59-68

  8. Mathematical Analysis

    • Haiyan Wang, Feng Wang, Kuai Xu
    Pages 69-112

  9. Applications

    • Haiyan Wang, Feng Wang, Kuai Xu
    Pages 113-132

  10. Back Matter

    Pages 133-144
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Keywords

About this book

The book lies at the interface of mathematics, social media analysis, and data science. Its authors aim to introduce a new dynamic modeling approach to the use of partial differential equations for describing information diffusion over online social networks. The eigenvalues and eigenvectors of the Laplacian matrix for the underlying social network are used to find communities (clusters) of online users. Once these clusters are embedded in a Euclidean space, the mathematical models, which are reaction-diffusion equations, are developed based on intuitive social distances between clusters within the Euclidean space. The models are validated with data from major social media such as Twitter. In addition, mathematical analysis of these models is applied, revealing insights into information flow on social media. Two applications with geocoded Twitter data are included in the book: one describing the social movement in Twitter during the Egyptian revolution in 2011 and another predicting influenza prevalence. The new approach advocates a paradigm shift for modeling information diffusion in online social networks and lays the theoretical groundwork for many spatio-temporal modeling problems in the big-data era.

Authors and Affiliations

  • School of Mathematical & Natural Sciences, Arizona State University, Glendale, USA

    Haiyan Wang, Feng Wang, Kuai Xu

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