Growing Protean Graphs

Online social networks have become ubiquitous to today's society and the study of data from these networks has improved our understanding of the processes by which relationships form. Research in statistical relational learning focuses on methods to exploit correlations among the attributes of linked nodes to predict user characteristics with greater accuracy. Concurrently, research on generative graph models has primarily focused on modeling network structure without attributes, producing several models that are able to replicate structural characteristics of networks such as power law degree distributions or community structure. However, there has been little work on how to generate networks with real-world structural properties and correlated attributes. In this work, we present the Attributed Graph Model (AGM) framework to jointly model network structure and vertex attributes. Our framework learns the attribute correlations in the observed network and exploits a generative graph model, such as the Kronecker Product Graph Model (KPGM) and Chung Lu Graph Model (CL), to compute structural edge probabilities. AGM then combines the attribute correlations with the structural probabilities to sample networks conditioned on attribute values, while keeping the expected edge probabilities and degrees of the input graph model. We outline an efficient method for estimating the parameters of AGM, as well as a sampling method based on Accept-Reject sampling to generate edges with correlated attributes. We demonstrate the efficiency and accuracy of our AGM framework on two large real-world networks, showing that AGM scales to networks with hundreds of thousands of vertices, as well as having high attribute correlation.

Diameter, connectivity, and phase transition of the uniform random intersection graph

Picture the life of a modern person in the western world: They wake up in the morning and check their social networking sites; they drive to work on roads that connect cities to each other; they make phone calls, send emails and messages to colleagues, friends, and family around the world; they use electricity flowing through power-lines; they browse the Internet, searching for information. All of these typical daily activities rely on the structure of networks. A network, in this case, is a set of nodes (people, web pages, etc) connected by edges (physical connection, collaboration, etc). The term graph is sometimes used to represent a more abstract structure - but here we use the terms graph and network interchangeably. The field of network analysis concerns studying and understanding networks in order to solve problems in the world around us. Graph models are used in conjunction with the study of real-world networks. They are used to study how well an algorithm may do on a real-world network, and for testing properties that may further produce faster algorithms. The first piece of this dissertation is an experimental study which explores features of real data, specifically power-law distributions in degrees and spectra. In addition to a comparison between features of real data to existing results in the literature, this study resulted in a hypothesis on power-law structure in spectra of real-world networks being more reliable than that in the degrees. The theoretical contributions of this dissertation are focused primarily on generating realistic networks through existing and novel graph models. The two graph models presented are called HyperKron and the Triangle Generalized Preferential Attachment model. Both of the models incorporate higher-order structure - leading to more sophisticated properties not examined in traditional models. We use the second of our models to further validate the hypothesis on power-laws in the spectra. Due to the structure of our model, we show that the power-law in the spectra is more resilient to sub-sampling. This gives some explanation for why we see power-laws more frequently in the spectra in real world data.

Web page clustering is a focal task in Web Mining to organize the content of websites, understanding their structure and discovering interactions among web pages. It is a tricky task since web pages have multiple dimension based on textual, hyperlink and HTML formatting (i.e. HTML tags and visual) properties. Existing algorithms use this information almost independently, mainly because it is difficult to combine them. This paper makes a contribution on clustering of web pages in a website by taking into account a distributional representation that combines all these features into a single vector space. The approach first crawls the website by using web pages’ HTML formatting and web lists in order to identify and represent the hyperlink structure by means of an adapted skip-gram model. Then, this hyperlink structure and the textual information are fused into a single vector space representation. The obtained representation is used to cluster websites using simultaneously their hyperlink structure and textual information. Experiments on real websites show that the proposed method improves clustering results.

The study of a national Web graph is challenging and can provide insight into social phenomena specific to a country. However, because there is no country border in the Web, deciding whether a web page belongs to that country or not is difficult. In this paper we aim at studying the characteristics of the Thai Web graph. We first address the challenge of gathering Thailand-related web pages from the borderless Web by proposing a set of criteria for defining Thailand-related web pages. Three Thai web snapshots have been collected during July 2004 (18M web pages), January 2007 (550K web pages), and May 2007 (1.4M web pages) respectively. We then analyze and report various statistical properties related to connectivity of the associated Thai Web graphs.

In previous articles we presented a PC based educational software on lexical analysis [1] and semantical analysis [4]. These systems were developed using an authoring system under MS Windows. The user can not change regular expressions or input words for nondeterministic respectively deterministic finite automata. To overcome these restrictions we developed GaniFA, our Java applet for visualization of algorithms from automata theory. It can be downloaded from our web page http://www.cs.uni-sb.de/GANIMAL as a JAR-file and requires a Java Plug-In 1.2. We invite the reader to use it in own web-based exercises, lecture notes or presentations on finite automata. Furthermore this web page gives a short overview, how this applet can be customized and embedded into HTML web pages.

Web pages often contain clutter (such as pop-up ads, unnecessary images and extraneous links) around the body of an article that distract a user from actual content.Extraction of "useful and relevant" content from web pages has many applications, including cell phone and PDA browsing, speech rendering for the visually impaired, and text summarization.Most approaches to removing clutter or making content more readable involve changing font size or removing HTML and data components such as images, which takes away from a webpage's inherent look and feel.Unlike "Content Reformatting", which aims to reproduce the entire webpage in a more convenient form, our solution directly addresses "Content Extraction".We have developed a framework that employs an easily extensible set of techniques that incorporate advantages of previous work on content extraction.Our key insight is to work with the Document Object Model tree, rather than with raw HTML markup.We have implemented our approach in a publicly available Web proxy to extract content from HTML web pages.

Webvise: browser and proxy support for open hypermedia structuring mechanisms on the World Wide Web

As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.

Network structures and graphs that feature the Small-World property have drawn a strong interest from the research community in two perspectives: 1) The Small-world effect is a popular phenomenon amongst several real-world complex networks; 2) Small-world graphs are considered veryuseful tools to model real-world complex networks as well as to design new topologies for certain applications in computer networks. We propose to study a new general random graph model that can be used to analyze the small-world effect (such an approach is already widely used). Our main result is to construct a general sufficient condition for this graph model to have logarithmic diameter, i.e. O(logn) for n as the number of the vertices. This result can help to assess and analyze several new graphs model for small-worlds

Feynman graph generation and propagator mixing, I

Due to the rapid growth of the number of digital images on the Web, there is an increasing demand for an effective and efficient method for organizing and retrieving the available images. This article describes iFind, a system for clustering and searching WWW images. By using a vision-based page segmentation algorithm, a Web page is partitioned into blocks, and the textual and link information of an image can be accurately extracted from the block containing that image. The textual information is used for image indexing. By extracting the page-to-block, block-to-image, block-to-page relationships through link structure and page layout analysis, we construct an image graph. Our method is less sensitive to noisy links than previous methods like PageRank, HITS, and PicASHOW, and hence the image graph can better reflect the semantic relationship between images. Using the notion of Markov Chain, we can compute the limiting probability distributions of the images, ImageRanks, which characterize the importance of the images. The ImageRanks are combined with the relevance scores to produce the final ranking for image search. With the graph models, we can also use techniques from spectral graph theory for image clustering and embedding, or 2-D visualization. Some experimental results on 11.6 million images downloaded from the Web are provided in the article.

Understanding overlapping community structures is crucial for network analysis and prediction. AGM (Affiliation Graph Model) is one of the favorite models for explaining the densely overlapped community structures. In this paper, we thoroughly re-investigate the assumptions made by the AGM model on real datasets. We find that the AGM model is not sufficient to explain several empirical behaviors observed in popular real-world networks. To our surprise, all our experimental results can be explained by a parameter-free hypothesis, leading to more straightforward modeling than AGM which has many parameters. Based on these findings, we propose a parameter-free Jaccard-based Affiliation Graph (JAG) model which models the probability of edge as a network specific constant times the Jaccard similarity between community sets associated with the individuals. Our modeling is significantly simpler than AGM, and it eliminates the need of associating a parameter, the probability value, with each community. Furthermore, JAG model naturally explains why (and in fact when) overlapping communities are densely connected. Based on these observations, we propose a new community-driven friendship formation process, which mathematically recovers the JAG model. JAG is the first model that points towards a direct causal relationship between tight connections in the given community with the number of overlapping communities inside it. Thus, the most effective way to bring a community together is to form more sub-communities within it. The community detection algorithm based on our modeling demonstrates a significantly simple algorithm with state-of-the-art accuracy on six real-world network datasets compared to the existing link analysis based methods.

. A statistical network model with overlapping communities can be generated as a superposition of mutually independent random graphs of varying size. The model is parameterized by the number of nodes, the number of communities, and the joint distribution of the community size and the edge probability. This model admits sparse parameter regimes with power-law limiting degree distributions and non-vanishing clustering coefficients. This article presents large-scale approximations of clique and cycle frequencies for graph samples generated by the model, which are valid for regimes with unbounded numbers of overlapping communities. Our results reveal the growth rates of these subgraph frequencies and show that their theoretical densities can be reliably estimated from the data.

Concentration of measure for the number of isolated vertices in the Erdős–Rényi random graph by size bias couplings