Modelling and Application of Dynamical Multilayer Social Networks

動態多層社交網絡上的建模與應用

Student thesis: Doctoral Thesis

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Award date3 Sep 2019

Abstract

A multilayer social network is a graph structure representing multiple social relationships among social entities. The relationships could be interactional, affective, economic, and political, and social entities could be individuals or organisations. The diversity of relationships and heterogeneity of social entities enable researchers to analyse and model dynamical multilayer social networks in a wide range of applications. The dynamical multilayer social networks are treated to two distinct concepts: dynamics of networks and dynamics on networks. But existing studies focus on the dynamics through one type of relationship, regardless of the intertwined effect of multiple relationships. Oversimplified relationships deflect the flow of dynamics. Motivated by the need to capture realistic dynamics, this thesis comprehensively studies the dynamics of and on multilayer social networks from topological analysis and strategic modelling to disease intervention and its simulation optimisation.

Topological analysis is a theoretical fundamental for modelling and further methodology development on multilayer social networks. We analysed the multilayer social networks with the metrics from micro to macro perspectives (i.e., clustering coefficient, the average length of shortest paths, degree correlation, overlap, pairwise multiplexity, and the proposed multilayer motif). The multilayer social networks have large clustering coefficients and small shortest path lengths. Multilayer social networks whose social relationships are more dependent have positive degree correlation, tremendous overlap, and large pairwise multiplexity. Besides, we extended the definition of motifs to multilayer motifs and analysed their occurrences in real-world multi-layer social networks. We found that multilayer motifs in social networks are homogeneous across layers, which indicates that different types of social relationships are reinforcing each other.

We observed that strongly dependent relationships consolidate individuals’ social position and reinforce barriers to new social interactions. While the weakly dependent relationships enforce individuals seek new social intersection. But the mechanism behind the observation remains obscure. Intending to understand the interplay effects of different relationships on social interactions, we formulate the behaviours of forming multiple relationships as a non-cooperative game. The individual in this game has to make a trade-off between the cost of establishing direct intralayer links and the potential decay benefits from intertwined intralayer and inter-layer links. We find, both through theoretical results and simulation results, that the equilibrium networks in this model have rich combinatorial structures and capture observed dynamics in the empirical study. In particular, large interplay effects encourage individuals to form links with friends of friends, and as a result, the complexity of the structure decreases; and vice versa.

As the multiplicity of complex relationships gives rises to unprecedented dynamics, the rich flows of dynamics can lead to the emergence of new critical properties such as the importance of nodes. Intending to studying the topological properties of individuals in multilayer social network and verifying their importance for intervention, we carried out a case study of Human Immunodeficiency Virus (HIV) transmission. A 2-layer social network framework is proposed to represent the unprotected sex and needle-sharing behaviours taken by female sex workers (FSWs) and persons who inject drugs (PWID), and each layer in the framework represents a different behaviour. Based on the framework, we estimated the scale and speed of HIV transmission under a set of intervention strategies isolating topologically essential individuals. Experimental results demonstrate that individuals who have critical positions processing intralayer and inter-layer spreading in a network are significant in escalating HIV transmissions.

Admitting that isolating individuals who are topologically significant could effectively slow the spreading process, it is not optimal. Research on allocating the limited resources on a subset of nodes to maximise or minimise the spread for multilayer social networks is still yet to come. Based on the aforementioned 2-layer social network framework, we propose a new random search method, named partition-based random search with network and memory prioritisation (PRS-NMP), to identify the optimal subset of high-value individuals in the network for HIV interventions. Numerical experiments demonstrate that the proposed PRS-NMP-based interventions could effectively reduce the scale of HIV transmission. The performances of PRS-NMP-based interventions are consistently better than the benchmark nested partition methods and network-based metrics.

This thesis focuses on modelling the dynamics of and on multilayer social networks and applying the network frameworks on HIV intervention, and it is organised into four parts. The first part is dedicated to capturing the patterns of multilayer relationships and their implications on the social network through multilayer motif analysis. The second part studies the evolution of multilayer relationships by proposing a game-theoretical network model. The third part develops a multilayer social network framework to capture the multi-mode HIV transmission among two key populations. The last part identifies the optimal subset of high-value individuals for HIV intervention in the proposed multilayer social network. Finally, I conclude with some open research directions on the topic of dynamical multilayer social networks, based on the findings of this thesis.

    Research areas

  • multilayer social network, non-cooperative model, disease transmssion, simulation optimisation