Twitter, a microblogging service less than three years old, commands more than 41 million users as of July 2009 and is growing fast. Twitter users tweet about any topic within the 140-character limit and follow others to receive their tweets. The goal of this paper is to study the topological characteristics of Twitter and its power as a new medium of information sharing. We have crawled the entire Twitter site and obtained 41.7 million user profiles, 1.47 billion social relations, 4, 262 trending topics, and 106 million tweets. In its follower-following topology analysis we have found a non-power-law follower distribution, a short effective diameter, and low reciprocity, which all mark a deviation from known characteristics of human social networks [28]. In order to identify influentials on Twitter, we have ranked users by the number of followers and by PageRank and found two rankings to be similar.

Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks. 1

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements organized into classes. Special attention is given to relating complex network analysis with the areas of pattern recognition and feature selection, as well as on surveying some concepts and measurements from traditional graph theory which are potentially useful for complex network research. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the

The study of complex social systems has traditionally been an arduous process, involving extensive surveys, interviews, ethnographic studies, or analysis of online behavior. Today, however, it is possible to use the unprecedented amount of information generated by pervasive mobile phones to provide insights into the dynamics of both individual and group behavior. Information such as continuous proximity, location, communication and activity data, has been gathered from the phones of 100 human subjects at MIT. Systematic measurements from these 100 people over the course of eight months have generated one of the largest datasets of continuous human behavior ever collected, representing over 300,000 hours of daily activity. In this thesis we describe how this data can be used to uncover regular rules and structure in behavior of both individuals and organizations, infer relationships between subjects, verify selfreport

We analyze the social network emerging from the user comment activity on the website Slashdot. The network presents common features of traditional social networks such as a giant component, small average path length and high clustering, but differs from them showing moderate reciprocity and neutral assortativity by degree. Using Kolmogorov-Smirnov statistical tests, we show that the degree distributions are better explained by log-normal instead of power-law distributions. We also study the structure of discussion threads using an intuitive radial tree representation. Threads show strong heterogeneity and self-similarity throughout the different nesting levels of a conversation. We use these results to propose a simple measure to evaluate the degree of controversy provoked by a post. Categories and Subject Descriptors

A central idea in marketing and diffusion research is that influentials—a minority of individuals who influence an exceptional number of their peers—are important to the formation of public opinion. Here we examine this idea, which we call the “influentials hypothesis,” using a series of computer simulations of interpersonal influence processes. Under most conditions that we consider, we find that large cascades of influence are driven not by influentials, but by a critical mass of easily influenced individuals. Although our results do not exclude the possibility that influentials can be important, they suggest that the influentials hypothesis requires more careful specification and testing than it has received.

Validation of mobile ad hoc network protocols relies almost exclusively on simulation. The value of the validation is, therefore, highly dependent on how realistic the movement models used in the simulations are. Since there is a very limited number of available real traces in the public domain, synthetic models for movement pattern generation must be used. However, most widely used models are currently very simplistic, their focus being ease of implementation rather than soundness of foundation. Simulation results of protocols are often based on randomly generated movement patterns and, therefore, may differ considerably from those that can be obtained by deploying the system in real scenarios. Movement is strongly affected by the needs of humans to socialise or cooperate, in one form or another. Fortunately, humans are known to associate in particular ways that can be mathematically modelled and that have been studied in social sciences for years. In this paper we propose a new mobility model founded on social network theory. The model allows collections of hosts to be grouped together in a way that is based on social relationships among the individuals. This clustering is then mapped to a topographical space, with movements influenced by the strength of social ties that may also change in time. We have validated our model with real traces by showing that the synthetic mobility traces are a very good approximation of human movement patterns. The impact of the adoption of the proposed algorithm on the performance of AODV and DSR is also presented and discussed. I.

A formal type of scientific and academic collaboration is coauthorship which can be represented by a coauthorship network. Coauthorship networks are among some of the largest social networks and offer us the opportunity to study the mechanisms underlying large-scale real world networks. We construct such a network for the Computer Science field covering research collaborations from 1980 to 2005, based on a large dataset of 451,305 papers authored by 283,174 distinct researchers. By mining this network, we first present a comprehensive study of the network statistical properties for a longitudinal network at the overall network level as well as for the intermediate community level. Major observations are that the database community is the best connected while the AI community is the most assortative, and that the Computer Science field as a whole shows a

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A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in which each vertex is given a random weight, and vertices with larger weights are more likely to be assigned large subsets. The distribution of the degree of a given vertex is characterized and is shown to depend on the weight of the vertex. In particular, if the weight distribution is a power law, the degree distribution will be so as well. Furthermore, an asymptotic expression for the clustering in the graph is derived. By tuning the parameters of the model, it is possible to generate a graph with arbitrary clustering, expected degree and – in the power law case – tail exponent.