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

Cultivating Communities of Practice: A Guide to Managing Knowledge

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

(2002). Getting to Yes: Negotiating Agreement without Giving in. Quality Management Journal: Vol. 9, No. 2, pp. 73-74.

Getting to Yes: Negotiating Agreement without Giving in

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

In this paper we present a novel strategy to discover the community structure of (possibly, large) networks This approach is based on the well-know concept of network modularity optimization To do so, our algorithm exploits a novel measure of edge centrality, based on the κ-paths This technique allows to efficiently compute a edge ranking in large networks in near linear time Once the centrality ranking is calculated, the algorithm computes the pairwise proximity between nodes of the network Finally, it discovers the community structure adopting a strategy inspired by the well-known state-of-the-art Louvain method (henceforth, LM), efficiently maximizing the network modularity The experiments we carried out show that our algorithm outperforms other techniques and slightly improves results of the original LM, providing reliable results Another advantage is that its adoption is naturally extended even to unweighted networks, differently with respect to the LM

/pdf/generalized-louvain-method-for-community-detection-in-large-4xjc137sjc.pdf

Generalized Louvain method for community detection in large networks

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

Strong ties connect individuals in the same community; weak ties connect individuals in different communities.

On Facebook, most ties are weak

We propose a modificationL 1 of the action description languageA. The languageL 1 allows representation of hypothetical situations and hypothetical occurrence of actions (as inA) as well as representation of actual occurrences of actions and observations of the truth values of fluents in actual situations. The corresponding entailment relation formalizes various types of common-sense reasoning about actions and their effects not modeled by previous approaches. As an application of L1 we also present an architecture for intelligent agents capable of observing, planning and acting in a changing environment based on the entailment relation of L1 and use logic programming approximation of this entailment to implement a planning module for this architecture. We prove the soundness of our implementation and give a sufficient condition for its completeness.

/pdf/representing-actions-laws-observations-and-hypotheses-3wgi7rzl25.pdf

Representing actions: Laws, observations and hypotheses

http://www.emilio.ferrara.name/wp-content/uploads/2011/06/jcss-2012.pdf

Alessandro Provetti

Papers

Generalized Louvain method for community detection in large networks

Crawling Facebook for Social Network Analysis Purposes

On Facebook, most ties are weak

Representing actions: Laws, observations and hypotheses

Mixing local and global information for community detection in large networks