The determination of node centrality is a fundamental topic in social network studies. As an addition to established metrics, which identify central nodes based on their brokerage power, the number and weight of their connections, and the ability to quickly reach all other nodes, we introduce five new measures of Distinctiveness Centrality. These new metrics attribute a higher score to nodes keeping a connection with the network periphery. They penalize links to highly-connected nodes and serve the identification of social actors with more distinctive network ties. We discuss some possible applications and properties of these newly introduced metrics, such as their upper and lower bounds. Distinctiveness centrality provides a viewpoint of centrality alternative to that of established metrics.
We demonstrate that individual behaviors directed at the attainment of distinctiveness can in fact produce complete social conformity. We thus offer an unexpected generative mechanism for this central social phenomenon. Specifically, we establish that agents who have fixed needs to be distinct and adapt their positions to achieve distinctiveness goals, can nevertheless self-organize to a limiting state of absolute conformity. This seemingly paradoxical result is deduced formally from a small number of natural assumptions, and is then explored at length computationally. Interesting departures f…
We study network centrality based on dynamic influence propagation models in social networks. To illustrate our integrated mathematical-algorithmic approach for understanding the fundamental interplay between dynamic influence processes and static network structures, we focus on two basic centrality measures: (a) Single Node Influence (SNI) centrality, which measures each node's significance by its influence spread; and (b) Shapley Centrality, which uses the Shapley value of the influence spread function --- formulated based on a fundamental cooperative-game-theoretical concept --- to measure …
Understanding the importance of links in transmitting information in a network can provide ways to hinder or postpone ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. In this work, we propose a new measure based on stochastic diffusion processes, the \textit{transmission centrality}, that captures the importance of links by estimating the average number of nodes to whom they transfer information during a global spreading diffusion process. We propose a simple algorithmic solution to compute transmission centrality and to approximate it in very large n…
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…
Centrality is an important notion in complex networks; it could be used to characterize how influential a node or an edge is in the network. It plays an important role in several other network analysis tools including community detection. Even though there are a small number of axiomatic frameworks associated with this notion, the existing formalizations are not generic in nature. In this paper we propose a generic axiomatic framework to capture all the intrinsic properties of a centrality measure (a.k.a. centrality index). We analyze popular centrality measures along with other novel measures…
The rapid expansion of social network provides a suitable platform for users to deliver messages. Through the social network, we can harvest resources and share messages in a very short time. The developing of social network has brought us tremendous conveniences. However, nodes that make up the network have different spreading capability, which are constrained by many factors, and the topological structure of network is the principal element. In order to calculate the importance of nodes in network more accurately, this paper defines the improved H-index centrality (IH) according to the diver…
Influence Maximization (IM) aims at finding the most influential users in a social network, i. e., users who maximize the spread of an opinion within a certain propagation model. Previous work investigated the correlation between influence spread and nodal centrality measures to bypass more expensive IM simulations. The results were promising but incomplete, since these studies investigated the performance (i. e., the ability to identify influential users) of centrality measures only in restricted settings, e. g., in undirected/unweighted networks and/or within a propagation model less common …
Centrality of a node measures its relative importance within a network. There are a number of applications of centrality, including inferring the influence or success of an individual in a social network, and the resulting social network dynamics. While we can compute the centrality of any node in a given network snapshot, a number of applications are also interested in knowing the potential importance of an individual in the future. However, current centrality is not necessarily an effective predictor of future centrality. While there are different measures of centrality, we focus on degree c…
Multi-layered social networks reflect complex relationships existing in modern interconnected IT systems. In such a network each pair of nodes may be linked by many edges that correspond to different communication or collaboration user activities. Multi-layered degree centrality for multi-layered social networks is presented in the paper. Experimental studies were carried out on data collected from the real Web 2.0 site. The multi-layered social network extracted from this data consists of ten distinct layers and the network analysis was performed for different degree centralities measures.
Measures of complex network analysis, such as vertex centrality, have the potential to unveil existing network patterns and behaviors. They contribute to the understanding of networks and their components by analyzing their structural properties, which makes them useful in several computer science domains and applications. Unfortunately, there is a large number of distinct centrality measures and little is known about their common characteristics in practice. By means of an empirical analysis, we aim at a clear understanding of the main centrality measures available, unveiling their similariti…
With its origin in sociology, Social Network Analysis (SNA), quickly emerged and spread to other areas of research, including anthropology, biology, information science, organizational studies, political science, and computer science. Being it's objective the investigation of social structures through the use of networks and graph theory, Social Network Analysis is, nowadays, an important research area in several domains. Social Network Analysis cope with different problems namely network metrics, models, visualization and information spreading, each one with several approaches, methods and al…
The problem of assigning centrality values to nodes and edges in graphs has been widely investigated during last years. Recently, a novel measure of node centrality has been proposed, called k-path centrality index, which is based on the propagation of messages inside a network along paths consisting of at most k edges. On the other hand, the importance of computing the centrality of edges has been put into evidence since 1970's by Anthonisse and, subsequently by Girvan and Newman. In this work we propose the generalization of the concept of k-path centrality by defining the k-path edge centra…
This paper proposes a new consensus model in participatory decision making. The model employs advice centrality approach by electing a leader and recommender named as Supra Decision Maker (SDM). A SDM has a role as a decision bench-marker to other decision makers in evaluating each alternative with respect to given criteria. The weighting value for each alternative can be obtained by considering consensus level and preferences' distances between SDM and other Decision Makers. A social function using Social Judgment Scheme (SJS) concept is employed when a decision does not achieve the required …
How does one find important or influential people in an online social network? Researchers have proposed a variety of centrality measures to identify individuals that are, for example, often visited by a random walk, infected in an epidemic, or receive many messages from friends. Recent research suggests that a social media users' capacity to respond to an incoming message is constrained by their finite attention, which they divide over all incoming information, i.e., information sent by users they follow. We propose a new measure of centrality --- limited-attention version of Bonacich's Alpha…
We perform social network analysis on 53 students split over three semesters and 13 groups, using conventional measures like eigenvector centrality, betweeness centrality, and degree centrality, as well as defining a variant of the Abelian Sandpile Model (ASM) with the intention of modeling stress propagation in the college classroom. We correlate the results of these analyses with group project grades received; due to a small or poorly collected dataset, we are unable to conclude that any of these network measures relates to those grades. However, we are successful in using this dataset to de…
Experts from several disciplines have been widely using centrality measures for analyzing large as well as complex networks. These measures rank nodes/edges in networks by quantifying a notion of the importance of nodes/edges. Ranking aids in identifying important and crucial actors in networks. In this chapter, we summarize some of the centrality measures that are extensively applied for mining social network data. We also discuss various directions of research related to these measures.
Centrality measures are crucial in quantifying the influence of the members of a social network. Although there has been a great deal of work dealing with this issue, the vast majority of classical centrality measures are agnostic of the community structure characterizing many social networks. Recent works have developed community-aware centrality measures that exploit features of the community structure information encountered in most real-world complex networks. In this paper, we investigate the interactions between 5 popular classical centrality measures and 5 community-aware centrality mea…
Measuring centrality in a social network, especially in bipartite mode, poses several challenges such as requirement of full knowledge of the network topology and lack of properly detection of top-k behavioral representative users. In this paper, to overcome the aforementioned challenging issues, we propose an accurate centrality measure, called HellRank, to identify central nodes in bipartite social networks. HellRank is based on the Hellinger distance between two nodes on the same side of a bipartite network. We theoretically analyze the impact of the Hellinger distance on a bipartite networ…
In social network analysis, there is a common perception that influence is relevant to determine the global behavior of the society and thus it can be used to enforce cooperation by targeting an adequate initial set of individuals or to analyze global choice processes. Here we propose centrality measures that can be used to analyze the relevance of the actors in process related to spread of influence. In [39] it was considered a multiagent system in which the agents are eager to perform a collective task depending on the perception of the willingness to perform the task of other individuals. T…
Several centrality measures have been formulated to quantify the notion of 'importance' of actors in social networks. Current measures scrutinize either local or global connectivity of the nodes and have been found to be inadequate for social networks. Ignoring hierarchy and community structure, which are inherent in all human social networks, is the primary cause of this inadequacy. Positional hierarchy and embeddedness of an actor in the community are intuitively crucial determinants of his importance. The theory of social capital asserts that an actor's importance is derived from his positi…
Identifying key nodes is crucial for accelerating or impeding dynamic spreading in a network. Community-aware centrality measures tackle this problem by exploiting the community structure of a network. Although there is a growing trend to design new community-aware centrality measures, there is no systematic investigation of the proposed measures' effectiveness. This study performs an extensive comparative evaluation of prominent community-aware centrality measures using the Susceptible-Infected-Recovered (SIR) model on real-world online social networks. Overall, results show that K-shell with…
The massive presence of silent members in online communities, the so-called lurkers, has long attracted the attention of researchers in social science, cognitive psychology, and computer-human interaction. However, the study of lurking phenomena represents an unexplored opportunity of research in data mining, information retrieval and related fields. In this paper, we take a first step towards the formal specification and analysis of lurking in social networks. We address the new problem of lurker ranking and propose the first centrality methods specifically conceived for ranking lurkers in so…
Mobile Social Networks (MSNs) have been evolving and enabling various fields in recent years. Recent advances in mobile edge computing, caching, and device-to-device communications, can have significant impacts on 5G systems. In those settings, identifying central users is crucial. It can provide important insights into designing and deploying diverse services and applications. However, it is challenging to evaluate the centrality of nodes in MSNs with dynamic environments. In this paper, we propose a Social-Relation based Centrality (SoReC) measure, in which social network information is used…
Facial appearance matters in social networks. Individuals frequently make trait judgments from facial clues. Although these face-based impressions lack the evidence to determine validity, they are of vital importance, because they may relate to human network-based social behavior, such as seeking certain individuals for help, advice, dating, and cooperation, and thus they may relate to centrality in social networks. However, little to no work has investigated the apparent facial traits that influence network centrality, despite the large amount of research on attributions of the central positi…
Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes in a network, a classical metric is centrality within which there are multiple specific instances including degree centrality, closeness centrality, betweenness centrality and more. As of today, existing algorithms to identify nodes with high centrality measures operate upon the entire (or rather global) network, resulting in high computational complexity. I…
Human communication is commonly represented as a temporal social network, and evaluated in terms of its uniqueness. We propose a set of new entropy-based measures for human communication dynamics represented within the temporal social network as event sequences. Using real world datasets and random interaction series of different types we find that real human contact events always significantly differ from random ones. This human distinctiveness increases over time and by means of the proposed entropy measures, we can observe sociological processes that take place within dynamic communities.
The position value, introduced by Meessen (1988), is a solution concept for cooperative games in which the value assigned to a player depends on the value of the connections or links he has with other players. This concept has been studied by Borm et al. (1992) and characterised by Slikker (2005). In this paper, we analyse the position value from the point of view of the typical properties of a measure of centrality in a social network. We extend the analysis already developed in Gomez et al. (2003) for the Myerson centrality measure, where the symmetric effect on the centralities of the end n…
This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, k-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high k-path centrality have high node betweenness centrality. The randomized algorithm runs in time $O(κ^{3}n^{2-2α}\log n)$ and outputs, for each vertex v, an estimate of its k-path centrality up to additive error of $\pm n^{1/2+ α}$ with probability $1-1/n^2$. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness…
Node centrality is one of the integral measures in network analysis with wide range of applications from socio-economic to personalized recommendation. We argue that an effective centrality measure should undertake stability even under information loss or noise introduced in the network. With six local information based centrality metric, we investigate the effect of varying assortativity while keeping degree distribution unchanged, using networks with scale free and exponential degree distribution. This model provides a novel scope to analyze stability of centrality metric which can further f…
This paper proposes a network model of opinion dynamics based on both the social network structure and network centralities. The conceptual novelty in this model is that the opinion of each individual is weighted by the associated network centrality in characterizing the opinion spread on social networks. Following a degree-centrality-weighted opinion dynamics model, we provide an algorithm to partition nodes of any graph into two and multiple clusters based on opinion disagreements. Furthermore, the partition algorithm is applied to real-world social networks including the Zachary karate club…
Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify various, widely used centrality concepts for vertices to those for edges, in order to find which edges in a network are important between other pairs of vertices. Focusing on the importance of edges, we propose an edge-centrality-based network decomposition technique to identify a hierarchy of sets of edges, where each set is associated with a different leve…
This paper introduces an evolutionary approach to enhance the process of finding central nodes in mobile networks. This can provide essential information and important applications in mobile and social networks. This evolutionary approach considers the dynamics of the network and takes into consideration the central nodes from previous time slots. We also study the applicability of maximal cliques algorithms in mobile social networks and how it can be used to find the central nodes based on the discovered maximal cliques. The experimental results are promising and show a significant enhancemen…
The online exchange of social recognition including, for instance, the Facebook "like" appears to produce a scarce allocation without a clear utility function defined for anyone involved. Given the importance attached to such digital commodities by both users and advertisers, it is of interest to study the forces governing their economics. Here we propose a centrality measure akin to eigenvector centrality to describe an individual's perceived importance in an online social network. It is shown in silico that strategically maximizing this prestige metric results in finite nontrivial rates of "…
The temporal component of social networks is often neglected in their analysis, and statistical measures are typically performed on a "static" representation of the network. As a result, measures of importance (like betweenness centrality) cannot reveal any temporal role of the entities involved. Our goal is to start filling this limitation by proposing a form of temporal betweenness measure, and by using it to analyse a knowledge mobilization network. We show that this measure, which takes time explicitly into account, allows us to detect centrality roles that were completely hidden in the cl…
Complex networks have gained more attention from the last few years. The size of real-world complex networks, such as online social networks, WWW network, collaboration networks, is increasing exponentially with time. It is not feasible to collect the complete data and store and process it. In the present work, we propose a method to estimate the degree centrality rank of a node without having the complete structure of the graph. The proposed algorithm uses the degree of a node and power-law exponent of the degree distribution to calculate the ranking. Simulation results on the Barabasi-Albert…
Online social networks are often subject to influence campaigns by malicious actors through the use of automated accounts known as bots. We consider the problem of detecting bots in online social networks and assessing their impact on the opinions of individuals. We begin by analyzing the behavior of bots in social networks and identify that they exhibit heterophily, meaning they interact with humans more than other bots. We use this property to develop a detection algorithm based on the Ising model from statistical physics. The bots are identified by solving a minimum cut problem. We show tha…
In this study we propose a method based on e-mail social network analysis to compare the communication behavior of managers who voluntarily quit their job and managers who decide to stay. Collecting 18 months of e-mail, we analyzed the communication behavior of 866 managers, out of which 111 left a large global service company. We compared differences in communication patterns by computing social network metrics, such as betweenness and closeness centrality, and content analysis indicators, such as emotionality and complexity of the language used. To study the emergence of managers' disengagem…
Social applications mine user social graphs to improve performance in search, provide recommendations, allow resource sharing and increase data privacy. When such applications are implemented on a peer-to-peer (P2P) architecture, the social graph is distributed on the P2P system: the traversal of the social graph translates into a socially-informed routing in the peer-to-peer layer. In this work we introduce the model of a projection graph that is the result of decentralizing a social graph onto a peer-to-peer network. We focus on three social network metrics: degree, node betweenness and edge…
Human social behavior plays a crucial role in how pathogens like SARS-CoV-2 or fake news spread in a population. Social interactions determine the contact network among individuals, while spreading, requiring individual-to-individual transmission, takes place on top of the network. Studying the topological aspects of a contact network, therefore, not only has the potential of leading to valuable insights into how the behavior of individuals impacts spreading phenomena, but it may also open up possibilities for devising effective behavioral interventions. Because of the temporal nature of inter…
Closeness centrality is one way of measuring how central a node is in the given network. The closeness centrality measure assigns a centrality value to each node based on its accessibility to the whole network. In real life applications, we are mainly interested in ranking nodes based on their centrality values. The classical method to compute the rank of a node first computes the closeness centrality of all nodes and then compares them to get its rank. Its time complexity is $O(n \cdot m + n)$, where $n$ represents total number of nodes, and $m$ represents total number of edges in the network…
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…
Cooperation played a significant role in the self-organization and evolution of living organisms. Both network topology and the initial position of cooperators heavily affect the cooperation of social dilemma games. We developed a novel simulation program package, called 'NetworGame', which is able to simulate any type of social dilemma games on any model, or real world networks with any assignment of initial cooperation or defection strategies to network nodes. The ability of initially defecting single nodes to break overall cooperation was called as 'game centrality'. The efficiency of this …
Identifying noteworthy spreaders in a network is essential for understanding the spreading process and controlling the reach of the spread in the network. The nodes that are holding more intrinsic power to extend the reach of the spread are important due to demand for various applications such as viral marketing, controlling rumor spreading or get a better understanding of spreading of the diseases. As an application of the viral marketing, maximization of the reach with a fixed budget is a fundamental requirement in the advertising business. Distributing a fixed number of promotional items fo…
Sampling from large networks represents a fundamental challenge for social network research. In this paper, we explore the sensitivity of different sampling techniques (node sampling, edge sampling, random walk sampling, and snowball sampling) on social networks with attributes. We consider the special case of networks (i) where we have one attribute with two values (e.g., male and female in the case of gender), (ii) where the size of the two groups is unequal (e.g., a male majority and a female minority), and (iii) where nodes with the same or different attribute value attract or repel each o…
School of Engineering and Computer Science, Morehead State University（莫尔黑德州立大学工程与计算机科学学院）
The goal of this research project is to analyze the dynamics of social networks using machine learning techniques to locate maximal cliques and to find clusters for the purpose of identifying a target demographic. Unsupervised machine learning techniques are designed and implemented in this project to analyze a dataset from YouTube to discover communities in the social network and find central nodes. Different clustering algorithms are implemented and applied to the YouTube dataset. The well-known Bron-Kerbosch algorithm is used effectively in this research to find maximal cliques. The results…
Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were proposed to account for the importance of the nodes of a network. In this paper, we try to provide a mathematically sound survey of the most important classic centrality measures known from the literature and propose an axiomatic approach to establish whether they are actually doing what they have been designed for. Our axioms suggest some simple, basic proper…
How to identify the influential spreaders in social networks is crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases and rumors, and so on. In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks. The comparison between the gravity centrality index and some well-known centralities, such as degree centrality, betweenn…
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…
Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of nodes. As there are many ways in which influence can be defined, many different centrality measures are in use. Parametrized centralities allow further flexibility and utility by tuning the centrality calculation to the regime most appropriate for a given network. Here, we identify two categories of centrality parameters. Reach parameters control the attenuation…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized approximation algorithm for centrality in weighted graphs. For graphs exhibiting the small world phenomenon, our method estimates the centrality of all vertices with high probability within a (1+epsilon) factor in near-linear time.
Real-world complex systems exhibit multiple levels of relationships. In many cases, they require to be modeled by interconnected multilayer networks, characterizing interactions on several levels simultaneously. It is of crucial importance in many fields, from economics to biology, from urban planning to social sciences, to identify the most (or the less) influent nodes in a network. However, defining the centrality of actors in an interconnected structure is not trivial. In this paper, we capitalize on the tensorial formalism, recently proposed to characterize and investigate this kind of com…
Complex network theory (CNT) is gaining a lot of attention in the scientific community, due to its capability to model and interpret an impressive number of natural and anthropic phenomena. One of the most active CNT field concerns the evaluation of the centrality of vertices and edges in the network. Several metrics have been proposed, but all of them share a topological point of view, namely centrality descends from the local or global connectivity structure of the network. However, vertices can exhibit their own intrinsic relevance independent from topology; e.g., vertices representing stra…
This study looks into employees' communication, offering novel metrics which can help to predict a company's stock price. We studied the intranet forum of a large Italian company, exploring the interactions and the use of language of about 8,000 employees. We built a network linking words included in the general discourse. In this network, we focused on the position of the node representing the company brand. We found that a lower sentiment, a higher betweenness centrality of the company brand, a denser word co-occurrence network and more equally distributed centrality scores of employees (low…
