We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We study the structure of the social graph of active Facebook users, the largest social network ever analyzed. We compute numerous features of the graph including the number of users and friendships, the degree distribution, path lengths, clustering, and mixing patterns. Our results center around three main observations. First, we characterize the global structure of the graph, determining that the social network is nearly fully connected, with 99.91% of individuals belonging to a single large connected component, and we confirm the "six degrees of separation" phenomenon on a global scale. Second, by studying the average local clustering coefficient and degeneracy of graph neighborhoods, we show that while the Facebook graph as a whole is clearly sparse, the graph neighborhoods of users contain surprisingly dense structure. Third, we characterize the assortativity patterns present in the graph by studying the basic demographic and network properties of users. We observe clear degree assortativity and characterize the extent to which "your friends have more friends than you". Furthermore, we observe a strong effect of age on friendship preferences as well as a globally modular community structure driven by nationality, but we do not find any strong gender homophily. We compare our results with those from smaller social networks and find mostly, but not entirely, agreement on common structural network characteristics.

https://snap.stanford.edu/class/cs224w-readings/backstrom12fb.pdf

The Anatomy of the Facebook Social Graph

Models and Methods in Social Network Analysis presents the most important developments in quantitative models and methods for analyzing social network data that have appeared during the 1990s. Intended as a complement to Wasserman and Faust’s Social Network Analysis: Methods and Applications, it is a collection of original articles by leading methodologists reviewing recent advances in their particular areas of network methods. Reviewed are advances in network measurement, network sampling, the analysis of centrality, positional analysis or blockmodeling, the analysis of diffusion through networks, the analysis of affiliation or “two-mode” networks, the theory of random graphs, dependence graphs, exponential families of random graphs, the analysis of longitudinal network data, graphic techniques for exploring network data, and software for the analysis of social networks.

/pdf/models-and-methods-in-social-network-analysis-46f9pqfov7.pdf

Models and methods in social network analysis

Linked: The New Science of Networks

In this paper, we review some advances made recently in the study of mobile phone datasets. This area of research has emerged a decade ago, with the increasing availability of large-scale anonymized datasets, and has grown into a stand-alone topic. We survey the contributions made so far on the social networks that can be constructed with such data, the study of personal mobility, geographical partitioning, urban planning, and help towards development as well as security and privacy issues.

/pdf/a-survey-of-results-on-mobile-phone-datasets-analysis-3ii9qbn03f.pdf

A survey of results on mobile phone datasets analysis

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.

/pdf/crawling-facebook-for-social-network-analysis-purposes-4wjt1ib1i1.pdf

Crawling Facebook for Social Network Analysis Purposes

The study of criminal networks using traces from heterogeneous communication media is acquiring increasing importance in nowadays society The usage of communication media such as mobile phones and online social networks leaves digital traces in the form of metadata that can be used for this type of analysis The goal of this work is twofold: first we provide a theoretical framework for the problem of detecting and characterizing criminal organizations in networks reconstructed from phone call records Then, we introduce an expert system to support law enforcement agencies in the task of unveiling the underlying structure of criminal networks hidden in communication data This platform allows for statistical network analysis, community detection and visual exploration of mobile phone network data It enables forensic investigators to deeply understand hierarchies within criminal organizations, discovering members who play central role and provide connection among sub-groups Our work concludes illustrating the adoption of our computational framework for a real-word criminal investigation

Detecting criminal organizations in mobile phone networks

/pdf/crawling-facebook-for-social-network-analysis-purposes-2pw0kzxouh.pdf

Crawling Facebook for social network analysis purposes

Network structure and resilience of Mafia syndicates

Online social networks (OSNs) are a unique web and social phenomenon, affecting tastes and behaviors of their users and helping them to maintain/create friendships. It is interesting to analyze the growth and evolution of online social networks both from the point of view of marketing and offer of new services and from a scientific viewpoint, since their structure and evolution may share similarities with real-life social networks. In social sciences, several techniques for analyzing (off-line) social networks have been developed, to evaluate quantitative properties (e.g., defining metrics and measures of structural characteristics of the networks) or qualitative aspects (e.g., studying the attachment model for the network evolution, the binary trust relationships, and the link prediction problem). However, OSN analysis poses novel challenges both to computer and Social scientists. We present our long-term research effort in analyzing Facebook, the largest and arguably most successful OSN today: it gathers more than 500 million users. Access to data about Facebook users and their friendship relations is restricted; thus, we acquired the necessary information directly from the front end of the website, in order to reconstruct a subgraph representing anonymous interconnections among a significant subset of users. We describe our ad hoc, privacy-compliant crawler for Facebook data extraction. To minimize bias, we adopt two different graph mining techniques: breadth-first-search (BFS) and rejection sampling. To analyze the structural properties of samples consisting of millions of nodes, we developed a specific tool for analyzing quantitative and qualitative properties of social networks, adopting and improving existing Social Network Analysis (SNA) techniques and algorithms.

/pdf/extraction-and-analysis-of-facebook-friendship-relations-1eaaujikaw.pdf

Salvatore Catanese

Papers

Crawling Facebook for Social Network Analysis Purposes

Detecting criminal organizations in mobile phone networks

Crawling Facebook for social network analysis purposes

Network structure and resilience of Mafia syndicates

Extraction and Analysis of Facebook Friendship Relations