We derive mean-field equations that describe the dynamics of a general model of rumor spreading on complex networks, and use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model on random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumor spreading rate below which a rumor cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumor spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumor, however, depends on the interplay between network topology and the rumor spreading rate. Our results show that scale-free networks are prone to the spreading of rumors, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale data dissemination algorithms on the Internet, the so-called gossip protocols.
Fractional-order SIS-UAU subdiffusion model for rumor propagation
Business College, Southwest University（西南大学商学院）；School of Journalism and Communication, Beijing Normal University（北京师范大学新闻传播学院）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Department of Physics, Humboldt University of Berlin（柏林洪堡大学物理系）；Faculty of Natural Sciences and Mathematics, University of Maribor（马里博尔大学自然科学与数学学院）；Community Healthcare Center Dr. Adolf Drolc Maribor（马里博尔阿道夫·德罗尔克博士社区医疗中心）；Department of Physics, Kyung Hee University（庆熙大学物理系）；University College, Korea University（韩国大学大学院）；College of Artificial Intelligence, Southwest University（西南大学人工智能学院）
Spreading dynamics on small-world networks with connectivity fluctuations and correlations
传染病和计算机恶意软件通过人与计算机之间的接触网络在人与计算机之间传播。这些网络具有连通性涨落、连通性相关和小世界特性。在以前的工作[A。Vazquez，Phys. Rev. Lett. 96，038702（2006）]我已经证明了连通性波动与小世界性质一起导致了一种新的传播规律，其特征在于初始幂律增长，其指数由网络上的平均节点距离确定。在这里，我将这些结果扩展到考虑在真实网络中通常观察到的连接相关性的影响。我表明，constitutive和disconstitutive连接的相关性增强和减少，分别，这种传播规律的有效性范围。作为一个推论，我得到的区域的连接波动和程度的相关性，其特征在于没有一个流行病的阈值。这些结果与传染病、谣言和信息在人类中的传播以及计算机病毒、电子邮件蠕虫和恶作剧在计算机用户中的传播有关。
