DySuse: Susceptibility Estimation in Dynamic Social Networks

Influence estimation aims to predict the total influence spread in social networks and has received surged attention in recent years. Most current studies focus on estimating the total number of influenced users in a social network, and neglect susceptibility estimation that aims to predict the probability of each user being influenced from the individual perspective. As a more fine-grained estimation task, susceptibility estimation is full of attractiveness and practical value. Based on the significance of susceptibility estimation and dynamic properties of social networks, we propose a task, called susceptibility estimation in dynamic social networks, which is even more realistic and valuable in real-world applications. Susceptibility estimation in dynamic networks has yet to be explored so far and is computationally intractable to naively adopt Monte Carlo simulation to obtain the results. To this end, we propose a novel end-to-end framework DySuse based on dynamic graph embedding technology. Specifically, we leverage a structural feature module to independently capture the structural information of influence diffusion on each single graph snapshot. Besides, {we propose the progressive mechanism according to the property of influence diffusion,} to couple the structural and temporal information during diffusion tightly. Moreover, a self-attention block {is designed to} further capture temporal dependency by flexibly weighting historical timestamps. Experimental results show that our framework is superior to the existing dynamic graph embedding models and has satisfactory prediction performance in multiple influence diffusion models.Comment: This paper has been published in Expert Systems With Application

A continuum limit for dense networks

Differential equations on metric graphs model disparate phenomena, including electron localisation in semiconductors, low-energy states of organic molecules, random laser networks, pollution diffusion in cities, dense neuronal networks and vasculature. This article describes the continuum limit of the edgewise Laplace operator on metric graphs, where vertices fill a given space densely, and the edge lengths shrink to zero (e.g. a spider web filling in a unit disc). We derive a new, coarse-grained partial differential operator which depends on the embedding space and local graph structure and has interesting similarities and differences with the Riemannian Laplace-Beltrami operator. We highlight various subtleties of dense metric graph systems with several semi- and fully analytic examples