text: Information cascades are ubiquitous in both physical society and online social media, taking on large variations in structures, dynamics and semantics. Although the dynamics and semantics of information cascades have been studied, the structural patterns and their correlations with dynamics and semantics are largely unknown. Here we explore a large-scale dataset including @math million information cascades with explicit records of spreading traces, spreading behaviors, information content as well as user profiles. We find that the structural complexity of information cascades is far beyond the previous conjectures. We first propose a ten-dimensional metric to quantify the structural characteristics of information cascades, reflecting cascade size, silhouette, direction and activity aspects. We find that bimodal law governs majority of the metrics, information flows in cascades have four directions, and the self-loop number and average activity of cascades follows power law. We then analyze the high-order structural patterns of information cascades. Finally, we evaluate to what extent the structural features of information cascades can explain its dynamic patterns and semantics, and finally uncover some notable implications of structural patterns in information cascades. Our discoveries also provide a foundation for the microscopic mechanisms for information spreading, potentially leading to implications for cascade prediction and outlier detection.
  @cite_4: 
  @cite_22: Viral products and ideas are intuitively understood to grow through a person-to-person diffusion process analogous to the spread of an infectious disease; however, until recently it has been prohibitively difficult to directly observe purportedly viral events, and thus to rigorously quantify or characterize their structural properties. Here we propose a formal measure of what we label “structural virality” that interpolates between two conceptual extremes: content that gains its popularity through a single, large broadcast and that which grows through multiple generations with any one individual directly responsible for only a fraction of the total adoption. We use this notion of structural virality to analyze a unique data set of a billion diffusion events on Twitter, including the propagation of news stories, videos, images, and petitions. We find that across all domains and all sizes of events, online diffusion is characterized by surprising structural diversity; that is, popular events regularly grow via both broadcast and viral mechanisms, as well as essentially all conceivable combinations of the two. Nevertheless, we find that structural virality is typically low, and remains so independent of size, suggesting that popularity is largely driven by the size of the largest broadcast. Finally, we attempt to replicate these findings with a model of contagion characterized by a low infection rate spreading on a scale-free network. We find that although several of our empirical findings are consistent with such a model, it fails to replicate the observed diversity of structural virality, thereby suggesting new directions for future modeling efforts. This paper was accepted by Lorin Hitt, information systems.
  @cite_1: 
  @cite_32: Models of networked diffusion that are motivated by analogy with the spread of infectious disease have been applied to a wide range of social and economic adoption processes, including those related to new products, ideas, norms and behaviors. However, it is unknown how accurately these models account for the empirical structure of diffusion over networks. Here we describe the diffusion patterns arising from seven online domains, ranging from communications platforms to networked games to microblogging services, each involving distinct types of content and modes of sharing. We find strikingly similar patterns across all domains. In particular, the vast majority of cascades are small, and are described by a handful of simple tree structures that terminate within one degree of an initial adopting "seed." In addition we find that structures other than these account for only a tiny fraction of total adoptions; that is, adoptions resulting from chains of referrals are extremely rare. Finally, even for the largest cascades that we observe, we find that the bulk of adoptions often takes place within one degree of a few dominant individuals. Together, these observations suggest new directions for modeling of online adoption processes.
  @cite_6: Social networks are of interest to researchers in part because they are thought to mediate the flow of information in communities and organizations. Here we study the temporal dynamics of communication using on-line data, including e-mail communication among the faculty and staff of a large university over a two-year period. We formulate a temporal notion of "distance" in the underlying social network by measuring the minimum time required for information to spread from one node to another -- a concept that draws on the notion of vector-clocks from the study of distributed computing systems. We find that such temporal measures provide structural insights that are not apparent from analyses of the pure social network topology. In particular, we define the network backbone to be the subgraph consisting of edges on which information has the potential to flow the quickest. We find that the backbone is a sparse graph with a concentration of both highly embedded edges and long-range bridges -- a finding that sheds new light on the relationship between tie strength and connectivity in social networks.
  @cite_24: How do blogs cite and influence each other? How do such links evolve? Does the popularity of old blog posts drop exponentially with time? These are some of the questions that we address in this work. Blogs (weblogs) have become an important medium of information because of their timely publication, ease of use, and wide availability. In fact, they often make headlines, by discussing and discovering evidence about political events and facts. Often blogs link to one another, creating a publicly available record of how information and influence spreads through an underlying social network. Aggregating links from several blog posts creates a directed graph which we analyze to discover the patterns of information propagation in blogspace, and thereby understand the underlying social network. Here we report some surprising findings of the blog linking and information propagation structure, after we analyzed one of the largest available datasets, with 45, 000 blogs and ≈ 2.2 million blog-postings. Our analysis also sheds light on how rumors, viruses, and ideas propagate over social and computer networks.
  @cite_19: Although information, news, and opinions continuously circulate in the worldwide social network, the actual mechanics of how any single piece of information spreads on a global scale have been a mystery. Here, we trace such information-spreading processes at a person-by-person level using methods to reconstruct the propagation of massively circulated Internet chain letters. We find that rather than fanning out widely, reaching many people in very few steps according to “small-world” principles, the progress of these chain letters proceeds in a narrow but very deep tree-like pattern, continuing for several hundred steps. This suggests a new and more complex picture for the spread of information through a social network. We describe a probabilistic model based on network clustering and asynchronous response times that produces trees with this characteristic structure on social-network data.
  @cite_27: 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.
  @cite_31: Many of the world's most popular websites catalyze their growth through invitations from existing members. New members can then in turn issue invitations, and so on, creating cascades of member signups that can spread on a global scale. Although these diffusive invitation processes are critical to the popularity and growth of many websites, they have rarely been studied, and their properties remain elusive. For instance, it is not known how viral these cascades structures are, how cascades grow over time, or how diffusive growth affects the resulting distribution of member characteristics present on the site. In this paper, we study the diffusion of LinkedIn, an online professional network comprising over 332 million members, a large fraction of whom joined the site as part of a signup cascade. First we analyze the structural patterns of these signup cascades, and find them to be qualitatively different from previously studied information diffusion cascades. We also examine how signup cascades grow over time, and observe that diffusion via invitations on LinkedIn occurs over much longer timescales than are typically associated with other types of online diffusion. Finally, we connect the cascade structures with rich individual-level attribute data to investigate the interplay between the two. Using novel techniques to study the role of homophily in diffusion, we find striking differences between the local, edge-wise homophily and the global, cascade-level homophily we observe in our data, suggesting that signup cascades form surprisingly coherent groups of members.
  @cite_12: When users post photos on Facebook, they have the option of allowing their friends, followers, or anyone at all to subsequently reshare the photo. A portion of the billions of photos posted to Facebook generates cascades of reshares, enabling many additional users to see, like, comment, and reshare the photos. In this paper we present characteristics of such cascades in aggregate, finding that a small fraction of photos account for a significant proportion of reshare activity and generate cascades of non-trivial size and depth. We also show that the true influence chains in such cascades can be much deeper than what is visible through direct attribution. To illuminate how large cascades can form, we study the diffusion trees of two widely distributed photos: one posted on President Barack Obama’s page following his reelection victory, and another posted by an individual Facebook user hoping to garner enough likes for a cause. We show that the two cascades, despite achieving comparable total sizes, are markedly different in their time evolution, reshare depth distribution, predictability of subcascade sizes, and the demographics of users who propagate them. The findings suggest not only that cascades can achieve considerable size but that they can do so in distinct ways.
summary: We presented related work in three dimensions: cascade structures, dynamics and topics. The cascade structures have been studied in different scenarios, including blogs @cite_1 @cite_24 @cite_27 , communication network @cite_6 , Facebook @cite_12 , Twitter @cite_32 , LinkedIn @cite_31 . , or to infer structures @cite_4 . Deep-tree structures are found and modeled in Ref. @cite_19 . Goel @cite_22 studied the virality of cascades by using Wiener index. However, we find information flows in cascades have four directions, indicating complex structures than tree patterns. Furthermore, ignoring the high-order correlations between structure metrics in previous studies prevent our understandings of cascade structures.