APS/EK10599 Weak Ties: Subtle Role in the Information Diffusion in Online Social Networks Jichang Zhao State Key Laboratory of Software Development Environment, Beihang University, Beijing 100191, P.R.China Junjie Wu Information Systems Department, School of Economics and Management, Beihang University, Beijing 100191, P.R.China Ke Xu ∗ State Key Laboratory of Software Development Environment, Beihang University, Beijing 100191, P.R.China (Dated: September 25, 2018) As a social media, online social networks play a vital role in the social information diffusion. However, due to its unique complexity, the mechanism of the diffusion in online social networks is different from the ones in other types of networks and remains unclear to us. Meanwhile, few works have been done to reveal the coupled dynamics of both the structure and the diffusion of online social networks. To this end, in this paper, we propose a model to investigate how the structure is coupled with the diffusion in online social networks from the view of weak ties. Through numerical experiments on large-scale online social networks, we find that in contrast to some previous research results, selecting weak ties preferentially to republish cannot make the information diffuse quickly, while random selection can achieve this goal. However, when we remove the weak ties gradually, the coverage of the information will drop sharply even in the case of random selection. We also give a reasonable explanation for this by extra analysis and experiments. Finally, we conclude that weak ties play a subtle role in the information diffusion in online social networks. On one hand, they act as bridges to connect isolated local communities together and break through the local trapping of the information. On the other hand, selecting them as preferential paths to republish cannot help the information spread further in the network. As a result, weak ties might be of use in the control of the virus spread and the private information diffusion in real-world applications. PACS numbers: 89.65.-s, 87.23.Ge, 89.70.-a, 89.75.-k arXiv:1001.3181v2 [cs.SI] 14 Dec 2010 content generating patterns [13, 15]. At the same time, some concepts and methods of traditional social networks have also been introduced into current researches: The strength of ties is one of them. The strength of ties was first proposed by Granovetter in his landmark paper [16] in 1973, in which he thought the strength of ties could be measured by the relative overlap of the neighborhood of two nodes in the network. It was interesting that dif- ferent from the common sense, he found that loose ac- quaintances, known as weak ties, were helpful in finding a new job [17]. This novel finding has become a hot topic of research for decades. In [18], a predictive model was proposed to map social media data to the tie strength. In [19], Onnela et al. gave a simple but quantified definition to the overlap of neighbors of nodes i and j as follows: The emergence of the Internet has changed the way of communication radically and, especially, the devel- opment of Web 2.0 applications has led to some ex- tremely popular online social sites, such as Facebook [1], Flickr [2], YouTube [3], Twitter [4], LiveJournal [5], Orkut [6] and Xiaonei [7]. These sites provide a powerful means of sharing information, finding content and orga- nizing contacts [8] for ordinary people. Users can consoli- date their existing relationships in the real world through publishing blogs, photos, messages and even states. They also have a chance to communicate with strangers that they have never met on the other end of the world. Based on the development and prevalence of the Internet, online social sites have reformed the structure of the traditional social network to a new complex system, called the online social network, which attracts a lot of research interests recently as a new social media. Recent works about online social networks mainly fo- cus on probing and collecting network topologies [8, 9], structural analysis [8–11], user interactions [12–14] and where c$_{ij}$ is the number of common acquaintances, k$_{i}$ and k$_{j}$ are the degrees of i and j , respectively. In this paper, we define w$_{ij}$ as the strength of the tie between i and j . The lower w$_{ij}$ is, the weaker the strength of tie between i and j is. As a social media, the core feature of online social networks is the information diffusion. However, the mechanism of the diffusion is different from traditional w$_{ij}$ = c$_{ij}$ k$_{i}$ − 1 + k$_{j}$ − 1 − c$_{ij}$ , (1) ∗ Electronic address: kexu@nlsde.buaa.edu.cn I. INTRODUCTION