We describe our work in the collection and analysis of massive data describing the connections between participants to online social networks. Alternative approaches to social network data collection are defined and evaluated in practice, against the popular Facebook Web site. Thanks to our ad-hoc, privacy-compliant crawlers, two large samples, comprising millions of connections, have been collected; the data is anonymous and organized as an undirected graph. We describe a set of tools that we developed to analyze specific properties of such social-network graphs, i.e., among others, degree distribution, centrality measures, scaling laws and distribution of friendship.
The classic work on social networks is rooted in the field of ; in late sixties Milgram and Travers @cite_17 introduced the well-known theories of the and the . Zachary @cite_4 , in his PhD thesis, formalized the first model of a real-life social network. Then, social networks started attracting the interest of different sciences, including Computer Science; for example Kleinberg @cite_12 studied the algorithmic aspects of social networks while @cite_7 analyzed their range of applicability.
@cite_4 @cite_7 @cite_12 @cite_17
2128678576 1964119857 2032005951 1977186326
Long a matter of folklore, the small-world phenomenon'''' --the principle that we are all linked by short chains of acquaintances --was inaugurated as an area of experimental study in the social sciences through the pioneering work of Stanley Milgram in the 1960''s. This work was among the first to make the phenomenon quantitative, allowing people to speak of the six degrees of separation'''' between any two people in the United States. Since then, a number of network models have been proposed as frameworks in which to study the problem analytically. One of the most refined of these models was formulated in recent work of Watts and Strogatz; their framework provided compelling evidence that the small-world phenomenon is pervasive in a range of networks arising in nature and technology, and a fundamental ingredient in the evolution of the World Wide Web. But existing models are insufficient to explain the striking algorithmic component of Milgram''s original findings: that individuals using local information are collectively very effective at actually constructing short paths between two points in a social network. Although recently proposed network models are rich in short paths, we prove that no decentralized algorithm, operating with local information only, can construct short paths in these networks with non-negligible probability. We then define an infinite family of network models that naturally generalizes the Watts-Strogatz model, and show that for one of these models, there is a decentralized algorithm capable of finding short paths with high probability. More generally, we provide a strong characterization of this family of network models, showing that there is in fact a unique model within the family for which decentralized algorithms are effective. In this classic book, first published in 1962, L. R. Ford, Jr., and D. R. Fulkerson set the foundation for the study of network flow problems. The models and algorithms introduced in Flows in Networks are used widely today in the fields of transportation systems, manufacturing, inventory planning, image processing, and Internet traffic. The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming. In addition, the book helped illuminate and unify results in combinatorial mathematics while emphasizing proofs based on computationally efficient construction. Flows in Networks is rich with insights that remain relevant to current research in engineering, management, and other sciences. This landmark work belongs on the bookshelf of every researcher working with networks. Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active "network community" and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online "networking communities" such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics. Sociologists since Simmel have been interested in social circles as essential features of friendship networks. Although network analysis has been increasingly used to uncover patterns among social relationships, theoretical explanations of these patterns have been inadequate. This paper presents a theory of the social organization of friendship ties. The approach is based upon Homans's concepts of activities, interactions, and sentiments and upon the concept of extra-network foci organizing social activities and interaction. The theory is contrasted with Heider's balance theory. Implications for transitivity, network bridges, and density of personal networks are discussed and presented as propositions. The focus theory is shown to help explain patterns of friendships in the 1965-66 Detroit Area Study. This paper is intended as a step toward the development of integrated theory to explain interrelationships between networks and other aspects of social structure. Implications for data analysis are discussed. Sociologists have long recognized the importance of patterns in networks of relations that connect individuals with each other. Simmel (1955) described modern society as consisting of loosely connected social circles of relationships. Granovetter (1973) has indicated the general significance of these social circles for communication, community organization, and social conflict. Various studies have supported this picture of the essential patterns in social networks, including Moreno's sociometry (1953), Milgram's "small world" experiments (1967), and Kadushin's observations (1966). Unfortunately, the study of social networks has often been carried out without concern for the origins in the larger social context. Most network analysis ends with description and labeling of patterns; and when explanations of patterns are offered, they frequently rely upon inherent tendencies within networks to become consistent, balanced, or transitive. As a consequence of such atheoretical and or self-contained network theoretical approaches, data are collected and data analysis techniques are devised for