小世界社會網絡演化模型：階段性需求於社交網絡拓樸動態的影響

Abstract

本研究提出一個以代理人為基礎，並結合個體階段式社交需求的小世界社會網絡模擬模型。模型中根據個體受社交吸引的各種因素，將各種因素依照個體階段的認知原則，歸納為不同層次的需求結構，建立出一個具階段式的需求金字塔模型。該模擬模型可分成五個階段層面：時空接近性、完整緊密性、正向相似性、連續權力性、邊際衰退性。模型各階段皆遵循不同的社交原則，透過動態演化方式形成的社會網絡是一個小世界複雜網絡，具有高群聚度與低分隔度二種在真實社會中常見的拓樸特性，並且滿足個體社交網絡中『富者益富』的普適現象，呈現無尺度性質—個體度分佈遵循冪次律，說明個體間社交關係發展的差異性。模型中透過代理人模擬真實社會中的人類個體，並以階段式需求金字塔來表現人類個體間的社交關係，充份呈現出人類社交行為的全貌。最後，以小世界性質的兩項評估指標，來進行模型各階段的敏感度分析，並透過找出社交關係的連結模式，暸解社交關係的各種傳播行為現象，並嘗試探討未來考量模擬虛擬社交型態的可能性。

The thesis presents an agent-based and small-world social network model combining individual hierarchy needs in the social network. Based on various factors, which gives impact on social behavior of individual, we classify these factors into different group and build up the pyramid model with hierarchy needs. These needs include five layers: space-time proximity, complete closure, positive similarity, status continuous, and marginal decline. This model is assumed to be changed continuously and formed a complicated social network with “small-world” and scale-free characteristics. First, the “small-world” has two well-known features: high clustering and low separation. Second, scale-free presents the feature of preferential attachment. That is, the fact the degree distribution of individual abides power-law explains the reason why the deviation of social relationship development exists among individuals. Besides, we also assume that agents act as individuals in the real world and have social relationship by the pyramid of hierarchy needs. From this thesis, we can conclude that our empirical results could reflect social behavior in the real world. Moreover, this thesis also provide sensitivity analysis to evaluate the impact of clustering and separation on the model and tries to the find out connected pattern to understand human propagation behavior for further research references.