The community-degree graph model and its implications on epidemic spread in social networks

Abstract

This thesis addresses the complexities of understanding and simulating network-dependent social processes, particularly focusing on the diffusion of information and the spread of epidemics. The primary aim is to specify the structure of interactions using random network models and to introduce a novel model, the Community-Degree Graph Model (CDGM), which encapsulates both degree and community structural features of social networks with a focus on dense community overlaps. This work seeks to provide a deeper understanding of social network formation and evolution, enhancing the accuracy of simulations for network processes, especially in replicating epidemic dynamics.

The study comprises two distinct analyses. The first evaluates the CDGM's alignment with the community structure and other network properties of Facebook and Twitter networks. Parameters are optimised using the Nelder-Mead optimisation technique, based on edge similarity and power-law behaviour. Community structures within the real-world networks and other models are identified using the Ego-Splitting framework and are further partitioned by the Label Propagation Method. Outcomes are evaluated using similarity metrics such as the Frobenius Norm, Dynamic Time Warping, and the Kolmogorov-Smirnov Statistic, summarised through a scoring system. The CDGM demonstrates balanced performance across all comparisons, aligning closely with both degree sequence and community size distribution observed in real-world networks.

The second analysis assesses the efficacy of various models in generating networks that simulate epidemic dynamics on Facebook. A dataset of 540,000 simulations, employing the Susceptible-Infected-Recovered (SIR) model, is generated and analysed across different values of the transmission rate (beta) and recovery rate (gamma) under various immunisation strategies. The transmission rate beta represents the probability of disease transmission between a susceptible and an infected individual, while the recovery rate gamma denotes the probability of an infected individual recovering and becoming immune. The resemblance is generally higher at elevated values of beta and gamma. The analysis also reveals that k-core decomposition significantly influences the effectiveness of replicating epidemic dynamics on Facebook, as identified through a Random Forest Regressor.

Furthermore, while both the Watts-Strogatz (WS) model and CDGM emerge as the top two models in capturing epidemic dynamics, the CDGM exhibits a more consistent performance than the WS model, indicating its potential application in epidemiological modelling. This thesis thus advances the understanding of complex network structures and their dynamic processes, providing valuable insights and tools for the field of network science. The CDGM, despite its challenges, emerges as a promising model for future exploration, with the potential to inspire further advancements in generating networks that accurately replicate real-world social networks.