The value of a social network is generally determined by its size and the connectivity of its nodes. But since some of the nodes may be fake ones and others that are dormant, the question of validating the node counts by statistical tests becomes important. In this paper we propose the use of the Benford's distribution to check on the trustworthiness of the connectivity statistics. Our experiments using statistics of both symmetric and asymmetric networks show that when the accumulation processes are random, the convergence to Benford's law is significantly better, and therefore this fact can be used to distinguish between processes which are randomly generated and those with internal dependencies.
Shaped by human movement, place connectivity is quantified by the strength of spatial interactions among locations. For decades, spatial scientists have researched place connectivity, applications, and metrics. The growing popularity of social media provides a new data stream where spatial social interaction measures are largely devoid of privacy issues, easily assessable, and harmonized. In this study, we introduced a global multi-scale place connectivity index (PCI) based on spatial interactions among places revealed by geotagged tweets as a spatiotemporal-continuous and easy-to-implement me…
Follower count is a factor that quantifies the popularity of celebrities. It is a reflection of their power, prestige and overall social reach. In this paper we investigate whether the social connectivity or the language choice is more correlated to the future follower count of a celebrity. We collect data about tweets, retweets and mentions of 471 Indian celebrities with verified Twitter accounts. We build two novel networks to approximate social connectivity of the celebrities. We study various structural properties of these two networks and observe their correlations with future follower co…
Interpersonal relationships are necessary for successful daily functioning and wellbeing. Numerous studies have demonstrated the importance of social connectivity for mental health, both through direct peer-to-peer influence and by the location of individuals within their social network. Passive monitoring using smartphones provides an advanced tool to map social networks based on the proximity between individuals. This study investigates the feasibility of using a smartphone app to measure and assess the relationship between social network metrics and mental health. The app collected Bluetoot…
\emph{Implicit Social Network} is a connected social structure among a group of persons, where two of them are linked if they have some common interest. One real\mbox{-}life example of such networks is the implicit social network among the customers of an online commercial house, where there exists an edge between two customers if they like similar items. Such networks are often useful for different commercial applications such as \textit{target advertisement}, \textit{viral marketing}, etc. In this article, we study two fundamental problems in this direction. The first one is that, given the …
Recent years saw an increased interest in modeling and understanding the mechanisms of opinion and innovation spread through human networks. Using analysis of real-world social data, researchers are able to gain a better understanding of the dynamics of social networks and subsequently model the changes in such networks over time. We developed a social network model that both utilizes an agent-based approach with a dynamic update of opinions and connections between agents and reflects opinion propagation and structural changes over time as observed in real-world data. We validate the model usi…
How people connect with one another is a fundamental question in the social sciences, and the resulting social networks can have a profound impact on our daily lives. Blau offered a powerful explanation: people connect with one another based on their positions in a social space. Yet a principled measure of social distance, allowing comparison within and between societies, remains elusive. We use the connectivity kernel of conditionally-independent edge models to develop a family of segregation statistics with desirable properties: they offer an intuitive and universal characteristic scale on s…
Social fragmentation caused by widening differences among constituents has recently become a highly relevant issue to our modern society. Theoretical models of social fragmentation using the adaptive network framework have been proposed and studied in earlier literature, which are known to either converge to a homogeneous, well-connected network or fragment into many disconnected sub-networks with distinct states. Here we introduced the diversities of behavioral attributes among social constituents and studied their effects on social network evolution. We investigated, using a networked agent-…
In typical online social networks, users are linked by symmetric friend relations and can define circles of friends based on shared interests. In this paper, we look at social networks where users form links subject to both friendships and shared interests. Our goal is to understand resilience of these networks in terms of connectivity when both nodes and links are allowed to fail. We derive a zero-one law as well as the asymptotically exact probability result for connectivity under both node and link failures. The results answer the question of how to set the network parameters such that reli…
Formation and fragmentation of networks is typically studied using percolation theory, but most previous research has been restricted to studying a phase transition in cluster size, examining the emergence of a giant component. This approach does not study the effects of evolving network structure on dynamics that occur at the nodes, such as the synchronization of oscillators and the spread of information, epidemics, and neuronal excitations. We introduce and analyze new link-formation rules, called Social Climber (SC) attachment, that may be combined with arbitrary percolation models to produ…
Social networks have an important role in an individual's health, with the propagation of health-related features through a network, and correlations between network structures and symptomatology. Using Bluetooth-enabled smartphones to measure social connectivity is an alternative to traditional paper-based data collection; however studies employing this technology have been restricted to limited sets of homogenous handsets. We investigated the feasibility of using the Bluetooth Low Energy (BLE) protocol, present on users' own smartphones, to measure social connectivity. A custom application w…
Universitàt Autónoma de Barcelona（巴塞罗那自治大学）；University of Western Australia（西澳大学）；Heriot Watt University（赫瑞瓦特大学）
The distribution of cultural variants in a population is shaped by both neutral evolutionary dynamics and by selection pressures, which include several individual cognitive biases, demographic factors and social network structures. The temporal dynamics of social network connectivity, i.e. the order in which individuals in a population interact with each other, has been largely unexplored. In this paper we investigate how, in a fully connected social network, connectivity dynamics, alone and in interaction with different cognitive biases, affect the evolution of cultural variants. Using agent-…
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…
Networks arising from social, technological and natural domains exhibit rich connectivity patterns and nodes in such networks are often labeled with attributes or features. We address the question of modeling the structure of networks where nodes have attribute information. We present a Multiplicative Attribute Graph (MAG) model that considers nodes with categorical attributes and models the probability of an edge as the product of individual attribute link formation affinities. We develop a scalable variational expectation maximization parameter estimation method. Experiments show that MAG mo…
We present a study of social networks based on the analysis of Brazilian and Portuguese family names (surnames). We construct networks whose nodes are names of families and whose edges represent parental relations between two families. From these networks we extract the connectivity distribution, clustering coefficient, shortest path and centrality. We find that the connectivity distribution follows an approximate power law. We associate the number of hubs, centrality and entropy to the degree of miscegenation in the societies in both countries. Our results show that Portuguese society has a h…
Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch an infectious disease, or consumers adopt a trendy electronics product are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a \textit{dynamic} structural equation model is adopted to capture the relationship between observed adoption times and the unknown edge weights. Assuming a slowly time-varying topo…
Recent approaches on elite identification highlighted the important role of {\em intermediaries}, by means of a new definition of the core of a multiplex network, the {\em generalised} $K$-core. This newly introduced core subgraph crucially incorporates those individuals who, in spite of not being very connected, maintain the cohesiveness and plasticity of the core. Interestingly, it has been shown that the performance on elite identification of the generalised $K$-core is sensibly better that the standard $K$-core. Here we go further: Over a multiplex social system, we isolate the community s…
In the context of Twitter, social capitalists are specific users trying to increase their number of followers and interactions by any means. These users are not healthy for the Twitter network since they flaw notions of influence and visibility. Indeed, it has recently been observed that they are real and active users that can help malicious users such as spammers gaining influence. Studying their behavior and understanding their position in Twitter is thus of important interest. A recent work provided an efficient way to detect social capitalists using two simple topological measures. Based o…
Wright State University（莱特州立大学）；Ohio State University（俄亥俄州立大学）；Weill Cornell University（威尔康奈尔大学）
With ubiquity of social media platforms, millions of people are sharing their online persona by expressing their thoughts, moods, emotions, feelings, and even their daily struggles with mental health issues voluntarily and publicly on social media. Unlike the most existing efforts which study depression by analyzing textual content, we examine and exploit multimodal big data to discern depressive behavior using a wide variety of features including individual-level demographics. By developing a multimodal framework and employing statistical techniques for fusing heterogeneous sets of features o…
Modern social networks frequently encompass multiple distinct types of connectivity information; for instance, explicitly acknowledged friend relationships might complement behavioral measures that link users according to their actions or interests. One way to represent these networks is as multi-layer graphs, where each layer contains a unique set of edges over the same underlying vertices (users). Edges in different layers typically have related but distinct semantics; depending on the application multiple layers might be used to reduce noise through averaging, to perform multifaceted analys…
Social aspects of connectivity and information dispersion are often ignored while weighing the potential of Internet of Things (IoT). In the specialized domain of Internet of Vehicles (IoV), Social IoV (SIoV) is introduced realization its importance. Assuming a more commonly acceptable standardization of Big Data generated by IoV, the social dimensions enabling its fruitful usage remains a challenge. In this paper, an agent-based model of information sharing between vehicles for context-aware recommendations is presented. The model adheres to social dimensions as that of human society. Some im…
Online social networks are growing and becoming denser. The social connections of a given person may have very high variability: from close friends and relatives to acquaintances to people who hardly know. Inferring the strength of social ties is an important ingredient for modeling the interaction of users in a network and understanding their behavior. Furthermore, the problem has applications in computational social science, viral marketing, and people recommendation. In this paper we study the problem of inferring the strength of social ties in a given network. Our work is motivated by a re…
A $k$-motif (or graphlet) is a subgraph on $k$ nodes in a graph or network. Counting of motifs in complex networks has been a well-studied problem in network analysis of various real-word graphs arising from the study of social networks and bioinformatics. In particular, the triangle counting problem has received much attention due to its significance in understanding the behavior of social networks. Similarly, subgraphs with more than 3 nodes have received much attention recently. While there have been successful methods developed on this problem, most of the existing algorithms are not scala…
Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences. However, real-life interactions among users are very complicated and user relations can be high-order. Hypergraph provides a natural way to model complex high-order relations, while its potentials for improving social recommendation are under-explored. In this paper, we fill this gap and propose a multi-channel hypergraph convolutional network to enhance socia…
The study of social networks --- where people are located, geographically, and how they might be connected to one another --- is a current hot topic of interest, because of its immediate relevance to important applications, from devising efficient immunization techniques for the arrest of epidemics, to the design of better transportation and city planning paradigms, to the understanding of how rumors and opinions spread and take shape over time. We develop a spatial social complex network (SSCN) model that captures not only essential connectivity features of real-life social networks, includin…
In this paper, our recently proposed mobile-conductance based analytical framework is extended to the sparse settings, thus offering a unified tool for analyzing information spreading in mobile networks. A penalty factor is identified for information spreading in sparse networks as compared to the connected scenario, which is then intuitively interpreted and verified by simulations. With the analytical results obtained, the mobility-connectivity tradeoff is quantitatively analyzed to determine how much mobility may be exploited to make up for network connectivity deficiency.
The different approaches developed to analyze the structure of complex networks have generated a large number of studies. In the field of social networks at least, studies mainly address the detection and analysis of communities. In this paper, we challenge these approaches and focus on nodes that have meaningful local interactions able to identify the internal organization of communities or the way communities are assembled. We propose an algorithm, ItRich, to identify this type of nodes, based on the decomposition of a graph into successive, less and less dense, layers. Our method is tested …
We introduce and discuss kinetic models of opinion formation on social networks in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion formation model is subsequently coupled with a kinetic model describing the spreading of popularity of a product on the web through a social network. Numerical experiments on the underlying kinetic models show a good qualitative agreement with some measured trends of hashtags on social media websites and illustrate how companies can take advantage of the network structure to obtain at best the advertisemen…
We propose and analyze a graph model to study the connectivity of interdependent networks. Two interdependent networks of arbitrary topologies are modeled as two graphs, where every node in one graph is supported by supply nodes in the other graph, and a node fails if all of its supply nodes fail. Such interdependence arises in cyber-physical systems and layered network architectures. We study the \emph{supply node connectivity} of a network: namely, the minimum number of supply node removals that would disconnect the network. We develop algorithms to evaluate the supply node connectivity give…
The resolution matrix is a mathematical tool for analyzing inverse problems such as computational imaging systems. When treating network connectivity estimation as an inverse problem, the resolution matrix describes the degree to which network nodes and edges can be resolved. This is useful both for quantifying robustness of the network estimate, as well as identifying correlated activity. In this report we analyze the resolution matrix for functional MRI data from the Human Connectome project. We find that common metrics of the resolution metric can be used to identify networked activity, tho…
In this Letter, we empirically study the influence of reciprocal links, in order to understand its role in affecting the structure and function of directed social networks. Experimental results on two representative datesets, Sina Weibo and Douban, demonstrate that the reciprocal links indeed play a more important role than non-reciprocal ones in both spreading information and maintaining the network robustness. In particular, the information spreading process can be significantly enhanced by considering the reciprocal effect. In addition, reciprocal links are largely responsible for the conne…
Rich-club, assortativity and clustering coefficients are frequently-used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the assortativity and clustering coefficients of a large network, which reveals that the rich-club connectivity is leveraged throughout the network. Our study suggests that more attention should be payed to the organization pattern of rich nodes, for the structure of a complex system as a whole is determined by the associations between the most influential individ…
It has been experimentally shown that communities in social networks tend to have a core-periphery topology. However, there is still a limited understanding of the precise structure of core-periphery communities in social networks including the connectivity structure and interaction rates between agents. In this paper, we use a game-theoretic approach to derive a more precise characterization of the structure of core-periphery communities.
Unified framework for measuring segregation resolves how social and geographical space jointly shape connections
Imperial College London（帝国理工学院）；Massachusetts Institute of Technology（麻省理工学院）；Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；Indian Institute of Technology Delhi（印度德里理工学院）
We use mobile device data to construct empirical interpersonal physical contact networks in the city of Portland, Oregon, both before and after social distancing measures were enacted during the COVID-19 pandemic. These networks reveal how social distancing measures and the public's reaction to the incipient pandemic affected the connectivity patterns within the city. We find that as the pandemic developed there was a substantial decrease in the number of individuals with many contacts. We further study the impact of these different network topologies on the spread of COVID-19 by simulating an…
We develop an analytical approach which provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two strongly different behaviors depending on the type - compact or non compact - of the random walk. In the case of non compact exploration, we show that the MFPT scales linearly with the inverse connectivity of the target, and is largely independent of the starting point. On the contrary, in the compact case the MFPT is controlled by the source-target distance, an…
Random key graphs represent topologies of secure wireless sensor networks that apply the seminal Eschenauer-Gligor random key predistribution scheme to secure communication between sensors. These graphs have received much attention and also been used in diverse application areas beyond secure sensor networks; e.g., cryptanalysis, social networks, and recommender systems. Formally, a random key graph with $n$ nodes is constructed by assigning each node $X_n$ keys selected uniformly at random from a pool of $Y_n$ keys and then putting an undirected edge between any two nodes sharing at least one…
Community detection is a fundamental task in social network analysis. In this paper, first we develop an endorsement filtered user connectivity network by utilizing Heider's structural balance theory and certain Twitter triad patterns. Next, we develop three Nonnegative Matrix Factorization frameworks to investigate the contributions of different types of user connectivity and content information in community detection. We show that user content and endorsement filtered connectivity information are complementary to each other in clustering politically motivated users into pure political commun…
The Eschenauer--Gligor (EG) random key predistribution scheme has been widely recognized as a typical approach to secure communications in wireless sensor networks (WSNs). However, there is a lack of precise probability analysis on the reliable connectivity of WSNs under the EG scheme. To address this, we rigorously derive the asymptotically exact probability of $k$-connectivity in WSNs employing the EG scheme with unreliable links represented by independent on/off channels, where $k$-connectivity ensures that the network remains connected despite the failure of any $(k-1)$ sensors or links. O…
