In Kleinberg's small-world network model, strong ties are modeled as deterministic edges in the underlying base grid and weak ties are modeled as random edges connecting remote nodes. The probability of connecting a node @math with node @math through a weak tie is proportional to @math , where @math is the grid distance between @math and @math and @math is the parameter of the model. Complex contagion refers to the propagation mechanism in a network where each node is activated only after @math neighbors of the node are activated. In this paper, we propose the concept of routing of complex contagion (or complex routing), where we can activate one node at one time step with the goal of activating the targeted node in the end. We consider decentralized routing scheme where only the weak ties from the activated nodes are revealed. We study the routing time of complex contagion and compare the result with simple routing and complex diffusion (the diffusion of complex contagion, where all nodes that could be activated are activated immediately in the same step with the goal of activating all nodes in the end). We show that for decentralized complex routing, the routing time is lower bounded by a polynomial in @math (the number of nodes in the network) for all range of @math both in expectation and with high probability (in particular, @math for @math and @math for @math in expectation), while the routing time of simple contagion has polylogarithmic upper bound when @math . Our results indicate that complex routing is harder than complex diffusion and the routing time of complex contagion differs exponentially compared to simple contagion at sweetspot.
Social and information networks and network diffusions have been extensively studied, and a comprehensive coverage has been provided by recent textbooks such as @cite_11 @cite_0 . In this section, we provide most related work in addition to the ones already discussed in the introduction.
@cite_0 @cite_11
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Diffusion of information, spread of rumors and infectious diseases are all instances of stochastic processes that occur over the edges of an underlying network. Many times networks over which contagions spread are unobserved, and such networks are often dynamic and change over time. In this paper, we investigate the problem of inferring dynamic networks based on information diffusion data. We assume there is an unobserved dynamic network that changes over time, while we observe the results of a dynamic process spreading over the edges of the network. The task then is to infer the edges and the dynamics of the underlying network. We develop an on-line algorithm that relies on stochastic convex optimization to efficiently solve the dynamic network inference problem. We apply our algorithm to information diffusion among 3.3 million mainstream media and blog sites and experiment with more than 179 million different pieces of information spreading over the network in a one year period. We study the evolution of information pathways in the online media space and find interesting insights. Information pathways for general recurrent topics are more stable across time than for on-going news events. Clusters of news media sites and blogs often emerge and vanish in matter of days for on-going news events. Major social movements and events involving civil population, such as the Libyan' s civil war or Syria' s uprise, lead to an increased amount of information pathways among blogs as well as in the overall increase in the network centrality of blogs and social media sites. Information spreading in online social communities has attracted tremendous attention due to its utmost practical values in applications. Despite that several individual-level diffusion data have been investigated, we still lack the detailed understanding of the spreading pattern of information. Here, by comparing information flows and social links in a blog community, we find that the diffusion processes are induced by three different spreading mechanisms: social spreading, self-promotion and broadcast. Although numerous previous studies have employed epidemic spreading models to simulate information diffusion, we observe that such models fail to reproduce the realistic diffusion pattern. In respect to users behaviors, strikingly, we find that most users would stick to one specific diffusion mechanism. Moreover, our observations indicate that the social spreading is not only crucial for the structure of diffusion trees, but also capable of inducing more subsequent individuals to acquire the information. Our findings suggest new directions for modeling of information diffusion in social systems, and could inform design of efficient propagation strategies based on users behaviors. Online social networks play a major role in the spread of information at very large scale. A lot of effort have been made in order to understand this phenomenon, ranging from popular topic detection to information diffusion modeling, including influential spreaders identification. In this article, we present a survey of representative methods dealing with these issues and propose a taxonomy that summarizes the state-of-the-art. The objective is to provide a comprehensive analysis and guide of existing efforts around information diffusion in social networks. This survey is intended to help researchers in quickly understanding existing works and possible improvements to bring. Predicting the diffusion of information on social networks is a key problem for applications like Opinion Leader Detection, Buzz Detection or Viral Marketing. Many recent diffusion models are direct extensions of the Cascade and Threshold models, initially proposed for epidemiology and social studies. In such models, the diffusion process is based on the dynamics of interactions between neighbor nodes in the network (the social pressure), and largely ignores important dimensions as the content of the piece of information diffused. We propose here a new family of probabilistic models that aims at predicting how a content diffuses in a network by making use of additional dimensions: the content of the piece of information diffused, user's profile and willingness to diffuse. These models are illustrated and compared with other approaches on two blog datasets. The experimental results obtained on these datasets show that taking into account the content of the piece of information diffused is important to accurately model the diffusion process.