Modeling Information Diffusion in Online Social Networks with Partial Differential Equations

by Haiyan Wang, Feng Wang, Kuai Xu

Overview

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.

Product Details

ISBN-13:	9783030388508
Publisher:	Springer International Publishing
Publication date:	03/17/2020
Series:	Surveys and Tutorials in the Applied Mathematical Sciences , #7
Edition description:	1st ed. 2020
Pages:	144
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

Ordinary Differential Equation Models on Social Networks.- Spatio-temporal Patterns of Information Diffusion.- Clustering of Online Social Network Graphs.- Partial Differential Equation Models.- Modeling Complex Interactions.- Mathematical Analysis.- Applications.