friends will republish it. Take Facebook as an example, in which News Feed and Live Feed are two significant and popular features. News Feed constantly updates a user’s profile page to list all his or her friends’ news in Facebook . The news includes conversations taking place between the walls of the user’s friends, changes of pro- file pages, events, and so on [27]. Live Feed facilitates the users to access the details of the contents updated by News Feed. It is updated in a real-time manner after the user’s login to the web [28]. In fact, News Feed aggre- gates the most interesting contents that a user’s friends are posting, while Live Feed shows to the user all the actions his or her friends are taking in Facebook [29]. If j is not in P , then add it to the set of nodes that will republish I in the next round, denoted by W . So W = W ∪ { j } . Repeat this step for R$_{i}$ times. It is easy to find from Eq. (3) that during the diffu- sion, the number of republishing nodes selected from the neighborhood of i is decided by k$_{i}$ and β . It is consistent with the real situation that the user with more friends tends to attract more other users to visit and republish the information. The more interesting or important the information is, the higher the chance that it will be re- published. We use parameter α in Eq. (4) to associate the diffusion with the strength of the ties, which means dif- ferent values of α will lead to different selections of ties as paths for republishing information in the next round. In fact, when α = − 1, weak ties are to be selected preferen- tially as paths for republishing. The selection is random when α = 0, and the strong ties will be selected with higher priority when α = 1. The feature of pushing and republishing we have dis- cussed above is indeed more obvious in Twitter , in which all the words you post will be pushed immediately to your followers’ terminals, including a PC or even a mo- bile phone, and then they can republish it if they like. However, in real-world situations, the trace of the infor- mation is hard to collect [25], especially for large-scale networks. So it is quite reasonable to build a model to characterize the mechanism and simulate the diffusion. Based on the procedure described above, we propose a simple model ID ( α, β ), where α is the navigating factor and β represents the strength of the information. In this model, α determines how to select neighbors to republish the information, while β ∈ [0 , 1] is a physical character of the information, which describes how interesting, novel, important, funny or resounding it is. The model is de- fined as follows: We define the fraction of nodes with the state σ 1 as the coverage of I , denoted by C . Since it is found that only 1-2% friends will republish the information in Flickr [25], we let β = 0 . 01 in the simulations. Fig. 3 shows the numeric experimental results on Facebook and YouTube networks. As can be seen, C reaches the maximum when α = 0. In other words, compared with weak or strong ties, selecting the republishing nodes randomly from the neighborhood will make the information spread faster and wider. This is indeed out of our expectation, since previous studies show that weak ties can facilitate the information diffusion in social networks. To understand this, we further explore the process of the information diffusion in details. By Eq. (1), we can easily have Assume that as k$_{j}$ increases, c$_{ij}$ increases proportion- ately, i.e., k$_{j}$/c$_{ij}$ = const . Then given a node i and its neighbor node j , we have k$_{j}$ ↑⇒ c$_{ij}$ ↑⇒ 1 /w$_{ij}$ ↓⇒ w$_{ij}$ ↑ , and vice versa. This implies that a neighbor node of i tends to have a higher degree if it has a stronger strength of ties with i . Therefore, when selecting the republishing nodes for the next round from the neighborhood, different α will select nodes with different degrees preferentially. For example, when α = − 1, the weak ties will be se- lected with higher priority, which means that the nodes with lower degrees will be selected preferentially. How- ever, it is easy to learn from Eq. (3) that, for the node with lower degree, the republishing nodes selected from its neighborhood will be less, which will eventually reduce R$_{i}$ = k$_{i}$β. (3) p$_{ij}$ = w α ij ∑ k i m $_{=1}$w α im . (4) • Step 1: Suppose there comes information I . Set the state of all the nodes in V to σ 0 . The state σ 0 of a node means I is not known to it, otherwise the state is σ 1 . • Step 2: Randomly select a seed node i from the network. The degree of i is k$_{i}$ . Set i to σ 1 . It publishes the information I with strength equal to β at time T = 0. • Step 3: Increase the time by one unit, i.e., T = T + 1. Set each node in the neighborhood of i to σ 1 . Add i to the set of nodes that have published I , denoted by P . So P = P ∪ { i } . • Step 4: Calculate the number of nodes that will republish I in the next round: • Step 5: Select one node j from the neighborhood of i with the probability [30] 1 /w$_{ij}$ = ( k$_{i}$ − 2) /c$_{ij}$ + k$_{j}$/c$_{ij}$ − 1 . C. Results and Analysis B. The Model for Information Diffusion • Step 6: For each node in W , execute from Step 3 to Step 5 recursively until W is null or all the nodes in V have known I . 4