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. Our goal is to build a model that generates realistic cascades, so that it can help us with link prediction and outlier detection. 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. Not only are blogs interesting on their own merit, but our analysis also sheds light on how rumors, viruses, and ideas propagate over social and computer networks. 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. We also present a simple model that mimics the spread of information on the blogosphere, and produces information cascades very similar to those found in real life.
How often do people create blog posts and links? Extensive work has been published on patterns relating to human behavior, which often generates bursty traffic. Disk accesses, network traffic, web-server traffic all exhibit burstiness. in @cite_15 provide fast algorithms for modeling such burstiness. Burstiness is often related to self-similarity, which was studied in the context of World Wide Web traffic @cite_17 . @cite_22 demonstrate the bursty behavior in web page visits and corresponding response times.
@cite_15 @cite_22 @cite_17
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Network, Web, and disk I O traffic are usually bursty and self-similar and therefore cannot be modeled adequately with Poisson arrivals. However, we wish to model these types of traffic and generate realistic traces, because of obvious applications for disk scheduling, network management, and Web server design. Previous models (like fractional Brownian motion and FARIMA, etc.) tried to capture the 'burstiness'. However, the proposed models either require too many parameters to fit and or require prohibitively large (quadratic) time to generate large traces. We propose a simple, parsimonious method, the b-model, which solves both problems: it requires just one parameter, and can easily generate large traces. In addition, it has many more attractive properties: (a) with our proposed estimation algorithm, it requires just a single pass over the actual trace to estimate b. For example, a one-day-long disk trace in milliseconds contains about 86 Mb data points and requires about 3 minutes for model fitting and 5 minutes for generation. (b) The resulting synthetic traces are very realistic: our experiments on real disk and Web traces show that our synthetic traces match the real ones very well in terms of queuing behavior. terized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution Pw w with =3 2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by = 1. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display = 1, the surface mail based communication belongs to the =3 2 universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.