We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at a distance from a given node. We also explore the degree distribution of for nodes at some distance from a given node. Implications for network sampling and diffusion on social networks are described.
The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed by the theory of random graphs with the nonlinear preferential attachment rule and the theory of Erdos-Renyi random graphs. In fact, well-calibrated network graph models and computer experiments with these models would help developers (owners) of the networks to predict their development correctly and to choose effective strategies for controlling network p…
In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics.
Estimation of social influence in networks can be substantially biased in observational studies due to homophily and network correlation in exposure to exogenous events. Randomized experiments, in which the researcher intervenes in the social system and uses randomization to determine how to do so, provide a methodology for credibly estimating of causal effects of social behaviors. In addition to addressing questions central to the social sciences, these estimates can form the basis for effective marketing and public policy. In this review, we discuss the design space of experiments to measure…
Analyzing social graphs with limited data access is challenging for third-party researchers. To address this challenge, a number of algorithms that estimate structural properties via a random walk have been developed. However, most existing algorithms are limited to the estimation of local structural properties. Here we propose a method for restoring the original social graph from the small sample obtained by a random walk. The proposed method generates a graph that preserves the estimates of local structural properties and the structure of the subgraph sampled by a random walk. We compare the…
Many online social networks feature restrictive web interfaces which only allow the query of a user's local neighborhood through the interface. To enable analytics over such an online social network through its restrictive web interface, many recent efforts reuse the existing Markov Chain Monte Carlo methods such as random walks to sample the social network and support analytics based on the samples. The problem with such an approach, however, is the large amount of queries often required (i.e., a long "mixing time") for a random walk to reach a desired (stationary) sampling distribution. In t…
Social graphs can be easily extracted from Online Social Networks. However these networks are getting larger from day to day. Sampling methods used to evaluate graph information cannot accurately extract graph properties. Furthermore Social Networks are limiting the access to their data, making the crawling process even harder. A novel approach on Random Sampling is proposed, considering both limitation and resources. We evaluate this proposal with 4 different settings on 5 different Test Graphs, crawled directly from Twitter. Through comparing the results we observe the pros and cons of its m…
We empirical study the signs' property in the directed signed social networks of Slashdot and Epinions by using an reshuffled approach. Through calculating the entropy $S_{out}$ and the giant component $G$, we find an interesting 90/10 phenomenon: each individual labels his/her neighbors as friends with $90\%$ or foes with $10\%$ uniformly random from the macroscopic perspective. We also find that the entropy $S_{out}$ is suppressed by the non-randomness of labeling sign. Our present work can prove how do the randomness and the non-randomness coexist in human behavior of labeling signs, qualit…
Spectral graph theory gives an algebraical approach to analyze the dynamics of a network by using the matrix that represents the network structure. However, it is not easy for social networks to apply the spectral graph theory because the matrix elements cannot be given exactly to represent the structure of a social network. The matrix element should be set on the basis of the relationship between persons, but the relationship cannot be quantified accurately from obtainable data (e.g., call history and chat history). To get around this problem, we utilize the universality of random matrix with…
How to enable efficient analytics over such data has been an increasingly important research problem. Given the sheer size of such social networks, many existing studies resort to sampling techniques that draw random nodes from an online social network through its restrictive web/API interface. Almost all of them use the exact same underlying technique of random walk - a Markov Chain Monte Carlo based method which iteratively transits from one node to its random neighbor. Random walk fits naturally with this problem because, for most online social networks, the only query we can issue through …
Social networks play a key role in studying various individual and social behaviors. To use social networks in a study, their structural properties must be measured. For offline social networks, the conventional procedure is surveying/interviewing a set of randomly-selected respondents. In many practical applications, inferring the network structure via sampling is too prohibitively costly. There are also applications in which it simply fails. For example, for optimal vaccination or employing influential spreaders for public health interventions, we need to efficiently and quickly target well-…
The massive amounts of data that social media generates has facilitated the study of online human behavior on a scale unimaginable a few years ago. At the same time, the much discussed apparent randomness with which people interact online makes it appear as if these studies cannot reveal predictive social behaviors that could be used for developing better platforms and services. We use two large social databases to measure the mutual information entropy that both individual and group actions generate as they evolve over time. We show that user's interaction sequences have strong deterministic …
This paper develops strategic foundations for an important statistical model of random networks with heterogeneous expected degrees. Based on this, we show how social networking services that subtly alter the costs and indirect benefits of relationships can cause large changes in behavior and welfare. In the model, agents who value friends and friends of friends choose how much to socialize, which increases the probabilities of links but is costly. There is a sharp transition from fragmented, sparse equilibrium networks to connected, dense ones when the value of friends of friends crosses a co…
We introduce a homogeneous pair approximation to the Naming Game (NG) model by deriving a six-dimensional ODE for the two-word Naming Game. Our ODE reveals the change in dynamical behavior of the Naming Game as a function of the average degree < k > of an uncorrelated network. This result is in good agreement with the numerical results. We also analyze the extended NG model that allows for presence of committed nodes and show that there is a shift of the tipping point for social consensus in sparse networks.
We show that strategy independent adaptations of random interaction networks can induce powerful mechanisms, ranging from the Red Queen to group selection, that promote cooperation in evolutionary social dilemmas. These two mechanisms emerge spontaneously as dynamical processes due to deletions and additions of links, which are performed whenever players adopt new strategies and after a certain number of game iterations, respectively. The potency of cooperation promotion, as well as the mechanism responsible for it, can thereby be tuned via a single parameter determining the frequency of link …
In this paper, we introduce a novel, general purpose, technique for faster sampling of nodes over an online social network. Specifically, unlike traditional random walk which wait for the convergence of sampling distribution to a predetermined target distribution - a waiting process that incurs a high query cost - we develop WALK-ESTIMATE, which starts with a much shorter random walk, and then proactively estimate the sampling probability for the node taken before using acceptance-rejection sampling to adjust the sampling probability to the predetermined target distribution. We present a novel…
This work is aimed at studying realistic social control strategies for social networks based on the introduction of random information into the state of selected driver agents. Deliberately exposing selected agents to random information is a technique already experimented in recommender systems or search engines, and represents one of the few options for influencing the behavior of a social context that could be accepted as ethical, could be fully disclosed to members, and does not involve the use of force or of deception. Our research is based on a model of knowledge diffusion applied to a ti…
The sensitivity of networks regarding the removal of vertices has been studied extensively within the last 15 years. A common approach to measure this sensitivity is (i) removing successively vertices by following a specific removal strategy and (ii) comparing the original and the modified network using a specific comparison method. In this paper we apply a wide range of removal strategies and comparison methods in order to study the sensitivity of medium-sized networks from real world and randomly generated networks. In the first part of our study we observe that social networks and web graph…
We study the behaviour of a Schelling-class system in which a fraction $f$ of spatially-fixed switching agents is introduced. This new model allows for multiple interpretations, including: (i) random, non-preferential allocation (\textit{e.g.} by housing associations) of given, fixed sites in an open residential system, and (ii) superimposition of social and spatial mobility in a closed residential system.\\ We find that the presence of switching agents in a segregative Schelling-type dynamics can lead to the emergence of intermediate patterns (\textit{e.g.} mixture of patches, fuzzy interface…
We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed and undirected edges and arbitrary degree-degree correlations. Our work extends previous theoretical developments for the undirected case, and we provide numerical support for our findings by investigating an example class of networks for which we are able to obtain closed-form expressions.
Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remain same throughout …
Online social networks (OSN) contain extensive amount of information about the underlying society that is yet to be explored. One of the most feasible technique to fetch information from OSN, crawling through Application Programming Interface (API) requests, poses serious concerns over the the guarantees of the estimates. In this work, we focus on making reliable statistical inference with limited API crawls. Based on regenerative properties of the random walks, we propose an unbiased estimator for the aggregated sum of functions over edges and proved the connection between variance of the est…
Online social networks are being increasingly used for analyzing various societal phenomena such as epidemiology, information dissemination, marketing and sentiment flow. Popular analysis techniques such as clustering and influential node analysis, require the computation of eigenvectors of the real graph's adjacency matrix. Recent de-anonymization attacks on Netflix and AOL datasets show that an open access to such graphs pose privacy threats. Among the various privacy preserving models, Differential privacy provides the strongest privacy guarantees. In this paper we propose a privacy preserv…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of social networks including common-interest networks, collaboration networks, and actor networks. Simply put, a random intersection graph is constructed by assigning each node a set of items in some random manner and then putting an edge between any two nodes that share a certain number of items. Broadly speaking, our work is about analyzing random intersection…
