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.

How do online conversations build? Is there a common model that human communication follows? In this work we explore these questions in detail. We analyze the structure of conversations in three different social datasets, namely, Usenet groups, Yahoo! Groups, and Twitter. We propose a simple mathematical model for the generation of basic conversation structures and then refine this model to take into account the identities of each member of the conversation.

Classifying nodes in networks is a task with a wide range of applications. It can be particularly useful in anomaly and fraud detection. Many resources are invested in the task of fraud detection due to the high cost of fraud, and being able to automatically detect potential fraud quickly and precisely allows human investigators to work more efficiently. Many data analytic schemes have been put into use; however, schemes that bolster link analysis prove promising. This work builds upon the belief propagation algorithm for use in detecting collusion and other fraud schemes. We propose an algorithm called SNARE (Social Network Analysis for Risk Evaluation). By allowing one to use domain knowledge as well as link knowledge, the method was very successful for pinpointing misstated accounts in our sample of general ledger data, with a significant improvement over the default heuristic in true positive rates, and a lift factor of up to 6.5 (more than twice that of the default heuristic). We also apply SNARE to the task of graph labeling in general on publicly-available datasets. We show that with only some information about the nodes themselves in a network, we get surprisingly high accuracy of labels. Not only is SNARE applicable in a wide variety of domains, but it is also robust to the choice of parameters and highly scalable-linearly with the number of edges in a graph.

How do real, weighted graphs change over time? What patterns, if any, do they obey? Earlier studies focus on unweighted graphs, and, with few exceptions, they focus on static snapshots. Here, we report patterns we discover on several real, weighted, time-evolving graphs. The reported patterns can help in detecting anomalies in natural graphs, in making link prediction and in providing more criteria for evaluation of synthetic graph generators. We further propose an intuitive and easy way to construct weighted, time-evolving graphs. In fact, we prove that our generator will produce graphs which obey many patterns and laws observed to date. We also provide empirical evidence to support our claims.

The vast majority of earlier work has focused on graphs which are both connected (typically by ignoring all but the giant connected component), and unweighted. Here we study numerous, real, weighted graphs, and report surprising discoveries on the way in which new nodes join and form links in a social network. The motivating questions were the following: How do connected components in a graph form and change over time? What happens after new nodes join a network -- how common are repeated edges? We study numerous diverse, real graphs (citation networks, networks in social media, internet traffic, and others); and make the following contributions: (a) we observe that the non-giant connected components seem to stabilize in size, (b) we observe the weights on the edges follow several power laws with surprising exponents, and (c) we propose an intuitive, generative model for graph growth that obeys observed patterns.

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.