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 projects.
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…
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-…
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…
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.
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…
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…
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…
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…
Twitter is one of the largest social networks using exclusively directed links among accounts. This makes the Twitter social graph much closer to the social graph supporting real life communications than, for instance, Facebook. Therefore, understanding the structure of the Twitter social graph is interesting not only for computer scientists, but also for researchers in other fields, such as sociologists. However, little is known about how the information propagation in Twitter is constrained by its inner structure. In this paper, we present an in-depth study of the macroscopic structure of th…
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…
Social relationships can be divided into different classes based on the regularity with which they occur and the similarity among them. Thus, rare and somewhat similar relationships are random and cause noise in a social network, thus hiding the actual structure of the network and preventing an accurate analysis of it. In this context, in this paper we propose a process to handle social network data that exploits temporal features to improve the detection of communities by existing algorithms. By removing random interactions, we observe that social networks converge to a topology with more pur…
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 …
We describe a Bayesian model for social learning of a random variable in which agents might observe each other over a directed network. The outcomes produced are compared to those from a model in which observations occur randomly over a complete graph. In both cases we observe a nontrivial level of observation which maximizes learning, though individuals have strong incentive to defect from the societal optimum. The implications of such competition over information commons are discussed.
We propose the notion of $k$-integration as a measure of equality of opportunity in social networks. A social network is $k$-integrated if there is a path of length at most $k$ between any two individuals, thus guaranteeing that everybody has the same network opportunities to find a job, a romantic partner, or valuable information. We compute the minimum number of bridges (i.e. edges between nodes belonging to different components) or central nodes (those which are endpoints to a bridge) required to ensure $k$-integration. The answer depends only linearly on the size of each component for $k=2…
Many popular measures used in social network analysis, including centrality, are based on the random walk. The random walk is a model of a stochastic process where a node interacts with one other node at a time. However, the random walk may not be appropriate for modeling social phenomena, including epidemics and information diffusion, in which one node may interact with many others at the same time, for example, by broadcasting the virus or information to its neighbors. To produce meaningful results, social network analysis algorithms have to take into account the nature of interactions betwe…
All societies have been much more bipolar over the past few years, particularly after the emergence of online social networks and media. In fact, the gap between the two ends of social spectrum is going to be even deeper after the spread of new media. In this circumstance, social polarization has been a growing concern among socialists and computer science experts because of the detrimental impact which online social networks can have on societies by adding fuel to the fire of extremism. Several types of research were conducted for proposing measures to calculate the controversy level in socia…
Viral marketing is becoming important due to the popularity of online social networks (OSNs). Companies may provide incentives (e.g., via free samples of a product) to a small group of users in an OSN, and these users provide recommendations to their friends, which eventually increases the overall sales of a given product. Nevertheless, this also opens a door for "malicious behaviors": dishonest users may intentionally give misleading recommendations to their friends so as to distort the normal sales distribution. In this paper, we propose a detection framework to identify dishonest users in O…
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.
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order structure of a network. Higher-order structures such as the edge embeddedness and the size of communities may play more important roles in many online social networks. In this paper, we provide empirical evidence on the existence of rich higherorder structural characteristics in online social networks, develop mathematical models to interpret and model these …
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…
Recent years have seen the world become a closely connected society with the emergence of different types of social networks. Online social networks have provided a way to bridge long distances and establish numerous communication channels which were not possible earlier. These networks exhibit interesting behavior under intentional attacks and random failures where different structural properties influence the resilience in different ways. In this paper, we perform two sets of experiments and draw conclusions from the results pertaining to the resilience of social networks. The first experime…
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 …
The goal of opinion maximization is to maximize the positive view towards a product, an ideology or any entity among the individuals in social networks. So far, opinion maximization is mainly studied as finding a set of influential nodes for fast content dissemination in a social network. In this paper, we propose a novel approach to solve the problem, where opinion maximization is achieved through efficient information spreading. In our model, multiple sources inject information continuously into the network, while the regular nodes with heterogeneous social learning abilities spread the info…
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…
We consider the domination number for on-line social networks, both in a stochastic network model, and for real-world, networked data. Asymptotic sublinear bounds are rigorously derived for the domination number of graphs generated by the memoryless geometric protean random graph model. We establish sublinear bounds for the domination number of graphs in the Facebook 100 data set, and these bounds are well-correlated with those predicted by the stochastic model. In addition, we derive the asymptotic value of the domination number in classical random geometric graphs.
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a random walk have been studied. However, existing algorithms do not consider private nodes who hide their neighbors in real social networks, leading to some practical problems. Here we design random walk-based algorithms to accurately estimate properties without any problems caused by private nodes. First, we design a random walk-based sampling algorithm that…
Analyzing social networks is challenging. Key features of relational data require the use of non-standard statistical methods such as developing system-specific null, or reference, models that randomize one or more components of the observed data. Here we review a variety of randomization procedures that generate reference models for social network analysis. Reference models provide an expectation for hypothesis-testing when analyzing network data. We outline the key stages in producing an effective reference model and detail four approaches for generating reference distributions: permutation,…
Random walk-based sampling methods are gaining popularity and importance in characterizing large networks. While powerful, they suffer from the slow mixing problem when the graph is loosely connected, which results in poor estimation accuracy. Random walk with jumps (RWwJ) can address the slow mixing problem but it is inapplicable if the graph does not support uniform vertex sampling (UNI). In this work, we develop methods that can efficiently sample a graph without the necessity of UNI but still enjoy the similar benefits as RWwJ. We observe that many graphs under study, called target graphs,…
Motivated by the need for novel robust approaches to modelling the Covid-19 epidemic, this paper treats a population of $N$ individuals as an inhomogeneous random social network (IRSN). The nodes of the network represent different types of individuals and the edges represent significant social relationships. An epidemic is pictured as a contagion process that changes daily, triggered on day $0$ by a seed infection introduced into the population. Individuals' social behaviour and health status are assumed to be random, with probability distributions that vary with their type. First a formulatio…
We study the locally-defined social capital metric of Palasek (2013) for determining individuals' prestige within an online social network. From it we derive an equivalent global measure by considering random walks over the network itself. This result inspires a novel expression quantifying the strategic desirability of a potential social connection. We show in silico that ideal social neighbors tend to satisfy a "big fish in a small pond" criterion and that the distribution of neighbor-desirability throughout a network is governed by anti-homophily.
We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into standard threshold models of behavior. In this way, we attempt to capture important aspects of fashions and general societal trends. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in the random and deterministic versions of the model. In the limit of a large, dense network, however, we show that the…
We consider pairwise Markov random fields which have a number of important applications in statistical physics, image processing and machine learning such as Ising model and labeling problem to name a couple. Our own motivation comes from the need to produce synthetic models for social networks with attributes. First, we give conditions for rapid mixing of the associated Glauber dynamics and consider interesting particular cases. Then, for pairwise Markov random fields with submodular energy functions we construct monotone perfect simulation.
We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-stat…
I find that several models for information sharing in social networks can be interpreted as age-dependent multi-type branching processes, and build them independently following Sewastjanow. This allows to characterize criticality in (real and random) social networks. For random networks, I develop a moment-closure method that handles the high-dimensionality of these models: By modifying the timing of sharing with followers, all users can be represented by a single representative, while leaving the total progeny unchanged. Thus I compute the exact popularity distribution, revealing a viral char…
The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling and analyzing social networks? We argue that unlike a random walk, which conserves the quantity diffusing on a network, many interesting social phenomena, such as the spread of information or disease on a social network, are fundamentally non-conservative. When an individual infects her neighbor with a virus, the total amount of infection increases. We class…
Activity-driven modeling has been recently proposed as an alternative growth mechanism for time varying networks, displaying power-law degree distribution in time-aggregated representation. This approach assumes memoryless agents developing random connections, thus leading to random networks that fail to reproduce two-nodes degree correlations and the high clustering coefficient widely observed in real social networks. In this work we introduce these missing topological features by accounting for memory effects on the dynamic evolution of time-aggregated networks. To this end, we propose an ac…
As social network analysis (SNA) has drawn much attention in recent years, one bottleneck of SNA is these network data are too massive to handle. Furthermore, some network data are not accessible due to privacy problems. Therefore, we have to develop sampling methods to draw representative sample graphs from the population graph. In this paper, Metropolis-Hastings Random Walk (MHRW) and Random Walk with Jumps (RWwJ) sampling strategies are introduced, including the procedure of collecting nodes, the underlying mathematical theory, and corresponding estimators. We compared our methods and exist…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number $R_0$ which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper we study the equilibrium of the social distancing game, in which individuals choose their social distancing level according to an a…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here, we present a time-varying network model where each node and the dynamical formation of ties are characterised by these two features. We study how these properties affect random walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable. We derive analytical solutions for the station…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random and deterministic versions of the model. In the limit of a large, dense network, however, we show that these dynamics coincide. We construct a general mean field theory for random networks and show this predicts that the dynamics on the network are a smoothed version of the average response function dynamics. Thus, the behavior of the system can range from ste…
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…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the relationship between actors inside the network. This approach is important to support predictions and the decision-making process in many real-world applications. The social network analysis methodology, which borrows approaches from graph theory provides several metrics that enabled us to measure specific properties of the networks. Some of the metrics calculations we…
We show that in a variant of the Minority Game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simple stochastic strategy. By imagining a social scenario where the agents can only guess about the number of excess people in the majority, we show that as long as the guess value is sufficiently close to the reality, the system can reach a state of full efficiency or minimum fluctuation. A continuous transition to less efficient condition is observed when the guess value becomes worse. Hence, people can op…
In this paper, we provide a review on both fundamentals of social networks and latent space modeling. The former discusses important topics related to network description, including vertex characteristics and network structure; whereas the latter articulates relevant advances in network modeling, including random graph models, generalized random graph models, exponential random graph models, and social space models. We discuss in detail several latent space models provided in literature, providing special attention to distance, class, and eigen models in the context of undirected, binary netwo…
Motivated by a real-life problem of sharing social network data that contain sensitive personal information, we propose a novel approach to release and analyze synthetic graphs in order to protect privacy of individual relationships captured by the social network while maintaining the validity of statistical results. A case study using a version of the Enron e-mail corpus dataset demonstrates the application and usefulness of the proposed techniques in solving the challenging problem of maintaining privacy \emph{and} supporting open access to network data to ensure reproducibility of existing …
At a time when information seekers first turn to digital sources for news and opinion, it is critical that we understand the role that social media plays in human behavior. This is especially true when information consumers also act as information producers and editors by their online activity. In order to better understand the effects that editorial ratings have on online human behavior, we report the results of a large-scale in-vivo experiment in social media. We find that small, random rating manipulations on social media submissions created significant changes in downstream ratings resulti…
Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here we make use of this data by investigating fluctuations in yearly usage frequencies of specific words that describe social and natural phenomena, as derived from books that were published over the course of the past two centuries. We show that the determination of the Hurst parameter by means of fractal analysis provides fundamental insights into the nature of long-range correlations contained in the culturomic trajectories, and by doing so, offers new inter…
How does one develop a new online community that is highly engaging to each user and promotes social interaction? A number of websites offer friend-finding features that help users bootstrap social networks on the website by copying links from an established network like Facebook or Twitter. This paper quantifies the extent to which such social bootstrapping is effective in enhancing a social experience of the website. First, we develop a stylised analytical model that suggests that copying tends to produce a giant connected component (i.e., a connected community) quickly and preserves propert…
Acceptance of an innovation can occur through mutliple exposures to individuals who have already accepted it. Presented here is a model to trace the evolution of an innovation in a social network with a preference $λ$, amidst topological constraints specified mainly by connectivity, $k$ and population size, $N_k$. With the interplay between properties of innovation and network structure, the model attempts to explain the variations in patterns of innovations across social networks. Time in which the propagation attains highest velocity depends on $λ^{-2}k^{-2}N_{k}^{1/2}$. Dynamics in random n…
Stanford University（斯坦福大学）；University of Zürich（苏黎世大学）
Most existing personalization systems promote items that match a user's previous choices or those that are popular among similar users. This results in recommendations that are highly similar to the ones users are already exposed to, resulting in their isolation inside familiar but insulated information silos. In this context, we develop a novel recommendation framework with a goal of improving information diversity using a modified random walk exploration of the user-item graph. We focus on the problem of political content recommendation, while addressing a general problem applicable to perso…
A social tagging system allows users to add arbitrary strings, called "tags", on a shared resource to organize and manage information. The Yule--Simon process, which has shown the ability to capture the population dynamics of social tagging behavior, does not handle the mechanism of new vocabulary creation because it assumes that new vocabulary creation is a Poisson-like random process. In this research, we focus on the mechanism of vocabulary creation from the microscopic perspective and discuss whether it also follows the random process assumed in the Yule--Simon process. To capture the micr…
