The Anatomy of a Scientific Rumor

The announcement of the discovery of a Higgs boson-like particle at CERN will be remembered as one of the milestones of the scientific endeavor of the 21st century. In this paper we present a study of information spreading processes on Twitter before, during and after the announcement of the discovery of a new particle with the features of the elusive Higgs boson on 4th July 2012. We report evidence for non-trivial spatio-temporal patterns in user activities at individual and global level, such as tweeting, re-tweeting and replying to existing tweets. We provide a possible explanation for the observed time-varying dynamics of user activities during the spreading of this scientific "rumor". We model the information spreading in the corresponding network of individuals who posted a tweet related to the Higgs boson discovery. Finally, we show that we are able to reproduce the global behavior of about 500,000 individuals with remarkable accuracy.Comment: 11 pages, 8 figure

Topological properties of P.A. random graphs with edge-step functions

In this work we investigate a preferential attachment model whose parameter is a function $f:\mathbb{N}\to[0,1]$ that drives the asymptotic proportion between the numbers of vertices and edges of the graph. We investigate topological features of the graphs, proving general bounds for the diameter and the clique number. Our results regarding the diameter are sharp when $f$ is a regularly varying function at infinity with strictly negative index of regular variation $-\gamma$. For this particular class, we prove a characterization for the diameter that depends only on $-\gamma$. More specifically, we prove that the diameter of such graphs is of order $1/\gamma$ with high probability, although its vertex set order goes to infinity polynomially. Sharp results for the diameter for a wide class of slowly varying functions are also obtained. The almost sure convergence for the properly normalized logarithm of the clique number of the graphs generated by slowly varying functions is also proved

Mesoscopic structure and social aspects of human mobility

The individual movements of large numbers of people are important in many contexts, from urban planning to disease spreading. Datasets that capture human mobility are now available and many interesting features have been discovered, including the ultra-slow spatial growth of individual mobility. However, the detailed substructures and spatiotemporal flows of mobility - the sets and sequences of visited locations - have not been well studied. We show that individual mobility is dominated by small groups of frequently visited, dynamically close locations, forming primary "habitats" capturing typical daily activity, along with subsidiary habitats representing additional travel. These habitats do not correspond to typical contexts such as home or work. The temporal evolution of mobility within habitats, which constitutes most motion, is universal across habitats and exhibits scaling patterns both distinct from all previous observations and unpredicted by current models. The delay to enter subsidiary habitats is a primary factor in the spatiotemporal growth of human travel. Interestingly, habitats correlate with non-mobility dynamics such as communication activity, implying that habitats may influence processes such as information spreading and revealing new connections between human mobility and social networks.Comment: 7 pages, 5 figures (main text); 11 pages, 9 figures, 1 table (supporting information

Hipsters on Networks: How a Small Group of Individuals Can Lead to an Anti-Establishment Majority

The spread of opinions, memes, diseases, and "alternative facts" in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread. In this paper, we explore how \textit{anti-establishment} nodes (e.g., \textit{hipsters}) influence the spreading dynamics of two competing products. We consider a model in which spreading follows a deterministic rule for updating node states (which describe which product has been adopted) in which an adjustable fraction $p_{\rm Hip}$ of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two. The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted. We simulate our model on both synthetic and real networks, and we show that the hipsters have a major effect on the final fraction of people who adopt each product: even when only one of the two products exists at the beginning of the simulations, a very small fraction of hipsters in a network can still cause the other product to eventually become the more popular one. To account for this behavior, we construct an approximation for the steady-state adoption fraction on $k$-regular trees in the limit of few hipsters. Additionally, our simulations demonstrate that a time delay $\tau$ in the knowledge of the product distribution in a population, as compared to immediate knowledge of product adoption among nearest neighbors, can have a large effect on the final distribution of product adoptions. Our simple model and analysis may help shed light on the road to success for anti-establishment choices in elections, as such success can arise rather generically in our model from a small number of anti-establishment individuals and ordinary processes of social influence on normal individuals.Comment: Extensively revised, with much new analysis and numerics The abstract on arXiv is a shortened version of the full abstract because of space limit

Distinguishing Infections on Different Graph Topologies

The history of infections and epidemics holds famous examples where understanding, containing and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV and most computer viruses, spread person to person, device to device, through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, do not. In this paper we study two fundamental questions of detection: first, given a snapshot view of a (perhaps vanishingly small) fraction of those infected, under what conditions is an epidemic spreading via contact (e.g., Influenza), distinguishable from a "random illness" operating independently of any contact network (e.g., seasonal allergies); second, if we do have an epidemic, under what conditions is it possible to determine which network of interactions is the main cause of the spread -- the causative network -- without any knowledge of the epidemic, other than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We derive sufficient conditions networks must satisfy for these problems to be identifiable, and produce efficient, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the grid, and the Erdos-Renyi graphs

Complex Contagions in Kleinberg's Small World Model

Complex contagions describe diffusion of behaviors in a social network in settings where spreading requires the influence by two or more neighbors. In a $k$-complex contagion, a cluster of nodes are initially infected, and additional nodes become infected in the next round if they have at least $k$ already infected neighbors. It has been argued that complex contagions better model behavioral changes such as adoption of new beliefs, fashion trends or expensive technology innovations. This has motivated rigorous understanding of spreading of complex contagions in social networks. Despite simple contagions ($k=1$) that spread fast in all small world graphs, how complex contagions spread is much less understood. Previous work~\cite{Ghasemiesfeh:2013:CCW} analyzes complex contagions in Kleinberg's small world model~\cite{kleinberg00small} where edges are randomly added according to a spatial distribution (with exponent $\gamma$) on top of a two dimensional grid structure. It has been shown in~\cite{Ghasemiesfeh:2013:CCW} that the speed of complex contagions differs exponentially when $\gamma=0$ compared to when $\gamma=2$. In this paper, we fully characterize the entire parameter space of $\gamma$ except at one point, and provide upper and lower bounds for the speed of $k$-complex contagions. We study two subtly different variants of Kleinberg's small world model and show that, with respect to complex contagions, they behave differently. For each model and each $k \geq 2$, we show that there is an intermediate range of values, such that when $\gamma$ takes any of these values, a $k$-complex contagion spreads quickly on the corresponding graph, in a polylogarithmic number of rounds. However, if $\gamma$ is outside this range, then a $k$-complex contagion requires a polynomial number of rounds to spread to the entire network.Comment: arXiv admin note: text overlap with arXiv:1404.266