Patterns on the Connected Components of Terabyte-Scale Graphs

Abstract

Abstract-How do connected components evolve? What are the regularities that govern the dynamic growth process and the static snapshot of the connected components? In this work, we study patterns in connected components of large, real-world graphs. First, we study one of the largest static Web graphs with billions of nodes and edges and analyze the regularities among the connected components using GFD(Graph Fractal Dimension) as our main tool. Second, we study several time evolving graphs and find dynamic patterns and rules that govern the dynamics of connected components. We analyze the growth rates of top connected components and study their relation over time. We also study the probability that a newcomer absorbs to disconnected components as a function of the current portion of the disconnected components and the degree of the newcomer. Finally, we propose a generative model that explains both the dynamic growth process and the static regularities of connected components.

FBM: A Flexible Random Walk Based Generative Model for Social Network

“…Different from others, McGlohon and Kang, et al proposed the Butterfly model and Community Connect model [25] based on random walk. Besides the different perspectives, two models are the same and they can simulate the majority of the found characteristics and patterns in the social network but there are some obvious shortcomings that the models can only generate social networks with fixed power-law exponents and lack effective methods to fit the models according to real data.…”

Guest editorial: special issue on data mining technologies for computational social science

“…At the macro-level, many important patterns of the global statistics of the underlying social networks have been discovered in the past, e.g., power-law distribution and small diameter (Albert et al 1999;Faloutsos et al 1999;Newman 2003), the frequent substructure (Xin et al 2005), the evolution and dynamics of social networks (Leskovec et al 2005;Kumar et al 2006), the dynamics of the on-line conversation (Kumar et al 2010), the connected and disconnected components of social networks (Kang et al 2010;McGlohon et al 2008), influence propagation (Kempe et al 2003;Leskovec et al 2007;Wang et al 2011b;Cui et al 2011), the group and community structure (Girvan and Newman;Backstrom et al 2006;Leskovec et al 2010), human mobility (González et al 2008;Wang et al 2011a), etc. There are also extensive work to study the social networks at the micro-level, e.g., ranking the importance of nodes (e.g., people) (Page et al 1998); proximity measure in social networks (Tong et al 2006), link prediction (Liben-Nowell and Kleinberg 2003), triangle counting (Leskovec et al 2008;Tsourakakis et al 2009), radius estimation and characterization (Kang et al 2011), etc.…”

Botnet detection using graph-based feature clustering

“…The static graphs can be further categorized into plain graphs and attributed graphs. Among the studies that use plain graphs for anomaly detection, Ding et al [34], Henderson et al [35], Henderson et al [36], Kang et al [37], Aggarwal [38], Zimek et al [39], Chen and Giles [40] and many more utilize structure based patterns to detect anomalies. On the other hand, studies done by Sun et al [41], Tong and Lin [42], Ambai et al [43], Nikulin and Huang [44] focus on the utilization of community based patterns to detect anomalies.…”