Influence in a large society: Interplay between information dynamics and network structure

L. Dolecek, D. Shah
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引用次数: 2

Abstract

Motivated by the recent emergence of large online social networks, we seek to understand the effects the underlying social network (graph) structure and the information dynamics have on the creation of influence of an individual. We examine a natural model for information dynamics under two important temporal scales: a first impression setting and a long— term or equilibrated setting. We obtain a characterization of relevant network structures under these temporal aspects, thereby allowing us to formalize the existence of influential agents. Specifically, we find that the existence of an influential agent corresponds to: (a) strictly positive information theoretic capacity over an infinite-sized noisy broadcast tree network in the first impression case, and (b) positive recurrent property of an appropriate (countable state space) Markov chain in the long-term case. As an application of our results, we evaluate the parameter space of the popular “small world” network model to identify when the network structure supports the existence of influential agents.
大社会中的影响:信息动态和网络结构之间的相互作用
受最近出现的大型在线社交网络的激励,我们试图理解潜在的社交网络(图)结构和信息动态对个人影响力产生的影响。我们在两个重要的时间尺度下研究信息动态的自然模型:第一印象设置和长期或平衡设置。我们在这些时间方面获得了相关网络结构的特征,从而使我们能够形式化有影响的代理人的存在。具体来说,我们发现一个有影响力的智能体的存在对应于:(a)在第一印象情况下,无限大小的噪声广播树网络上的严格正信息理论容量,以及(b)在长期情况下,适当的(可数状态空间)马尔可夫链的正循环性质。作为我们研究结果的一个应用,我们评估了流行的“小世界”网络模型的参数空间,以识别网络结构何时支持有影响力的代理的存在。
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