Social network is a main tunnel of rumor spreading. Previous studies are concentrated on a static rumor spreading. The content of the rumor is invariable during the whole spreading process. Indeed, the rumor evolves constantly in its spreading proces
s, which grows shorter, more concise, more easily grasped and told. In an early psychological experiment, researchers found about 70% of details in a rumor were lost in the first 6 mouth-to-mouth transmissions cite{TPR}. Based on the facts, we investigate rumor spreading on social networks, where the content of the rumor is modified by the individuals with a certain probability. In the scenario, they have two choices, to forward or to modify. As a forwarder, an individual disseminates the rumor directly to its neighbors. As a modifier, conversely, an individual revises the rumor before spreading it out. When the rumor spreads on the social networks, for instance, scale-free networks and small-world networks, the majority of individuals actually are infected by the multi-revised version of the rumor, if the modifiers dominate the networks. Our observation indicates that the original rumor may lose its influence in the spreading process. Similarly, a true information may turn to be a rumor as well. Our result suggests the rumor evolution should not be a negligible question, which may provide a better understanding of the generation and destruction of a rumor.
The studies based on $A+A rightarrow emptyset$ and $A+Brightarrow emptyset$ diffusion-annihilation processes have so far been studied on weighted uncorrelated scale-free networks and fractal scale-free networks. In the previous reports, it is widely
accepted that the segregation of particles in the processes is introduced by the fractal structure. In this paper, we study these processes on a family of weighted scale-free networks with identical degree sequence. We find that the depletion zone and segregation are essentially caused by the disassortative mixing, namely, high-degree nodes tend to connect with low-degree nodes. Their influence on the processes is governed by the correlation between the weight and degree. Our finding suggests both the weight and degree distribution dont suffice to characterize the diffusion-annihilation processes on weighted scale-free networks.
Explicit determination of the mean first-passage time (MFPT) for trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e. node with the hi
ghest degree), which are simultaneously scale-free and small-world. We obtain the precise analytic expression for the MFPT that is confirmed by direct numerical calculations. In the large system size limit, the MFPT approximately grows as a power-law function of the number of nodes, with the exponent much less than 1, which is significantly different from the scaling for some regular networks or fractals, such as regular lattices, Sierpinski fractals, T-graph, and complete graphs. The Apollonian network is the most efficient configuration for transport by diffusion among all previously studied structure.
