How to measure influence in social networks?

How to measure influence in social networks? Ana Carolina Ribeiro ✉ 1[0000-0003-1557-654X], Bruno Azevedo2[0000-0003-1494-4726], Jorge Oliveira e Sá2[0000-0003-4095-3431], and Ana Alice Baptista2[0000-0003-3525-0619] 1,2Centro ALGORITMI, University of Minho, 4800-058, Guimarães, Portugal 1[email protected] 2[email protected], [email protected], [email protected] Abstract. Today, social networks are a valued resource of social data that can be used to understand the interactions among people and communities. People can influence or be influenced by interactions, shared opinions and emotions. However, in the social network analysis, one of the main problems is to find the most influential people. This work aims to report on the results of literature review whose goal was to identify and analyse the metrics, algorithms and models used to measure the user influence on social networks. The search was carried out in three databases: Scopus, IEEEXplore, and ScienceDirect. We restricted published articles between the years 2014 until 2020, in English, and we used the following keywords: social networks analysis, influence, metrics, measurements, and algorithms. Backward process was applied to complement the search considering inclusion and exclusion criteria. As a result of this process, we obtained 25 articles: 12 in the initial search and 13 in the backward process. The literature review resulted in the collection of 21 influence metrics, 4 influence algorithms, and 8 models of influence analysis. We start by defining influence and presenting its properties and applications. We then proceed by describing, analysing and categorizing all that were found metrics, algorithms, and models to measure influence in social networks. Finally, we present a discussion on these metrics, algorithms, and models. This work helps researchers to quickly gain a broad perspective on metrics, algorithms, and models for influence in social networks and their relative potentialities and limitations. Keywords: Influence Metrics, Influence Analysis, Social Networks Analysis. 1 Introduction Networks are one of the fundamental structures of our complex systems. In the evolution of our cultural information systems, networks are a ubiquitous way to represent the dynamics of economic and social systems [1]–[4]. The Web allowed simultaneously the exponential production and spreading of digital information. Users are "prosumers", meaning that they are simultaneous interchangeably producers and consumers of information [5]. Social networks exponentially increased the number of social actors that create a wide number of connections forming 2 a vast structure of links between actors and other entities (e.g. documents, messages, posts, recommendations) [6]. The growing use of social networks has attracted many researchers, academics, and organizations to explore social network research topics, including the influence analysis [7]. Influence analysis and its spread on social networks have an important application value [8] by allowing to analyse and explain people's social behaviors. It also provide a theoretical basis for decision making [9]. However, there are still some challenges to work on [8]: there is no mathematical formula of influence; it is difficult to identify the parameters to measure the influence; and, the large amount of data generated by social networks, makes it difficult to analyse and, consequently, to determine the influence. An influence analysis study covers the study of influence properties such as influence evaluation metrics and algorithms, influence maximization, and social data collection and big data analysis [10]. This paper falls within the scope of the project 6,849.32 New Scientific Journal Articles Everyday: Visualize or Perish! [11] and the main objective of this work is to identify and analyse the most relevant and metrics, algorithms and/or influence models currently available. The articles’ search and selection process was based on the recommendations given by [12] complemented by [13] and was following: 1. Search engines and databases: Scopus, IEEEXplore, and ScienceDirect; 2. Time constraints: January 2014 to January 2020; 3. Keywords: social networks analysis, influence, algorithms, metrics, and measurements; 4. Types of documents: reviews, journals and conference papers; 5. Languages: English; 6. Selection criteria: Iterative process where the titles, abstracts and parts of the articles were reviewed for inclusion/exclusion. The search resulted in 12 articles. The backward process was applied to these articles, which resulted in an addition of 13 articles, totalling 25 articles. The main contributions of this work are briefly summarized bellow: 1. A methodology sufficiently detailed to allow the analysis of this study by other reliable researchers and use this study as a basis for future research into the influence on social networks. 2. An overview of the most relevant and up-to-date metrics, algorithms and/or models in social networks: 21 metrics, 4 algorithms, and 8 models of influence analysis. The remaining of this article is organized as follows: the section “Methodological Procedure” presents the methodology applied for the selection of articles; the section “Related Work” presents some the related works that analyse the algorithms, metrics, and models of influence; the section “A landscape of influence in social networks” aims to present the overview of the metrics, algorithms, and influence models, the section “Discussion” presents the discussion of the results obtained, and section “Conclusions and Future Work” presents the conclusions, limitations, and some future research directions. 3 2 Methodological Procedures This section reports the methodological procedures applied and that were based on [12]. Fig. 1 represents all stages of the process. 2.1 Initial search The initial search starts with the selection of three databases: Scopus, IEEEXplore, and ScienceDirect. These databases have wide coverage of articles related to the topic and allow to filter the results: according to [14], in the social sciences, the coverage of Scopus is much higher than that of the Web of Science; The percentage of titles covered only by Scopus is above 60%, to which is added the almost 40% coverage overlap (Scopus and WoS), with WoS alone covering a very small percentage of titles; Sources indexed only by WoS are not necessarily disposable, however, it is safe to use only Scopus. IEEExplore and Science Direct were used because they are widely used databases in the area of information systems, as a cross-check measure with Scopus results. The keywords used were “social networks analysis”, “influence”, “algorithms”, “measurements”, and “metrics”. In the initial search, we applied four search queries Fig. 1 - Methodology of literature review. 4 (SQ) (Fig. 1) with the following results: Scopus 2,552 articles, IEEEXplore 225 articles, and ScienceDirect 13,079 articles, totalling 15,856 articles. Considering these values, we used filters to get an acceptable number of results to analyse articles for all search queries: articles published from January 2014 to January 2020, conferences or journals or reviews, and written in English. However, according to the results obtained, it was necessary to adapt these filters for some search queries applied in some digital libraries, namely: • For search query 1 on Scopus, we applied a different filter concerning the document type: we selected reviews because the values collected in the initial search were very high (2,121 articles). The reviews were selected because this type of articles describe, analyse, and discuss scientific knowledge already published. • For search queries 3 and 4 applied on IEEEXplore, the values collected were low (6 and 9, respectively), and the application of filters was not necessary. After applying the filters, all articles collected from Scopus, IEEEXplore, and ScienceDirect will be analysed in the next section. 2.2 Articles selection process and results After the articles collected in the previous phase, in this phase, all articles will be analysed according to the inclusion and exclusion criteria (Table 1), in parallel with the three phases described below 1. Title and abstract: Articles were selected if the title and abstract were aligned with the research objectives; 2. Introduction and conclusion: The introduction and conclusion of the articles accepted in phase 1 were analysed to proceed to a new selection; 3. Full article: The articles accepted in phase 2 were then fully read and subset was selected to be included in the review. This process allowed the selection of 12 articles. We then applied a backward process were the references of the twelve previously selected articles were analysed. The implementation of the backward process resulted in the addition of 13 articles. The backward process, which allowed the identification of the most used metrics, algorithms and models to measure the influence on social networks, worked as a complemented the selection process, by allowing to gain a broader perspective on the topic. In total, 25 articles were collected and analysed. Table 1. Inclusion and Exclusion criteria. Inclusion criteria Exclusion criteria Articles about algorithms or metrics of social networks analysis. Articles not using metrics and/or influence algorithms (mention only metrics used in the social networks analysis, but not oriented to the analysis of influence); Articles about the algorithms or metrics to computing influence on a social network. Articles focused on the influence that social networks have on people's lives, education, family life and, in general, on society. Articles about the algorithms or metrics to computing influence maximization on a social network. Articles about the algorithms or metrics to computing influence diffusion on a social network. Articles about the algorithms or metrics to computing influence applied on a social network. 5 3 Related Work In this section, are reviewed the related works that analyse the algorithms, metrics, and models of influence. The work reported in [15], presents a research on the latest generation of models, methods, and aspects of evaluation associated to influence analysis and provides a comprehensive analysis, helps to understand social behaviours, provides a theoretical basis to influence public opinion and reveal future directions of research and possible applications. The authors distinguish models in two types: microscopic (linear threshold, independent cascade, etc.) and macroscopic (epidemic models are the most common). The authors consider that, in the future, the microscopic models should concentrate on considering human interactions and different mechanisms during the information diffusion, while the macroscopic models consider the same probability of transmission and identical influential power for all users. Differently, the authors of [8], present the state of the art on the influence analysis on social networks, presenting an overview of social networks, an explanation on the influence analysis at different levels, as a definition , properties, architecture and diffusion models, discuss the assessment metrics for influence and summarize the models for evaluating influence on social networks. In this work, the authors present some of the future trends in this topic that must be taken into account: the integration of crossdisciplinary knowledge due to the complexity of the topic; the development of an effective mechanism for influence analysis (hybrid approaches to improve the efficiency and effectiveness of influence analysis) and an effective model for the efficiency and scalability of influence analysis. The study [16] is also a relevant work because it focuses on the problem of predicting influential users on social networks. In this work, the authors present a three-level hierarchy that classifies the measures of influence: models, types, and algorithms. The authors also compare, based on empirical analysis, in terms of performance, precision, and correlation the measures of influence using a data set from two different social networks to verify the feasibility of measuring the influence. The results of the study show that the prediction of influential users does not depend only on the measures of influence, but also on the nature of social networks. In the article [17], the authors study the probability of an individual being an influencer. They grouped the influence measures in some categories: measures derived from the neighbourhood (that is, number of influencers, personal exposure of the network), diversity structural, temporal measures, cascade measures, and metadata. Also, they evaluated how these measures relate to the likelihood that a user will be influenced using actual data from a microblog. Subsequently, the authors evaluated the performance of these measures when used as a resource in a machine learning approach and compared performance in a variety of supervised machine learning approaches. Finally, they evaluated how the proportion of positive to negative samples in training and testing affects the results of predictions - still allowing the practical use of these concepts for applications of influence. 6 4 A landscape of influence in social networks This section starts by presenting the concept of influence on social networks and, some influence analysis applications, and their main properties. Also presented are the various metrics, algorithms and models found in the literature for influence analysis. For each metric, we present its definition and, in some cases, the calculation formula. 4.1 Understanding Influence in Social Networks In social sciences, the term influence is widely used: according to [18], influence is “The power to change or affect someone or something: the power to cause changes without directly forcing them to happen”; and [19], “social influence occurs when an individual’s thoughts, feelings or actions are affected by other people.” p.184. A social network can be represented as a graph G = (V, E), where V corresponds to the nodes (vertices) in the graph (users), and E corresponds to the edges that indicate the relationship between users [20], [21]. According to [20] the relationship (edges) connects the influencer and influenced node, i.e., who influences whom. The edges' weights correspond to the influence probabilities among the nodes. Marketing is one of the areas were influence analysis is most frequent. These specialists select a set of influential users and try to influence them to adopt a new behavior, product or service; Later, they expect these users to recommend to others, for example, by spreading word-of-mouth in the social networks [22]. In sentiment analysis, text mining tools and natural language processing to allow extract subjective information from data sets of social networks, for example, users' opinions and attitudes. This makes, it possible to analyse the influence of users [23]. Another interesting application is the influence analysis of academics in their communities. High impact researchers are not necessarily influential [24], [25]. According to [7], influence has the following properties: A user's influence can increase or decrease with new experiences or interactions – dynamic nature. These new experiences or interactions can be more important, and the old ones can become irrelevant over time, i.e., the user can stop being influential at any time; In a social network, information can be propagated from one user to another, allowing the development of chains of influence - propagative nature; Influence has no mathematical definition or measure. Its subjective nature leads to the personalization of the calculation of influence, where the biases and preferences of influencers have a direct impact on its calculation. To measure the influence on social networks, several metrics, algorithms, and models are known. These are grouped in the following categories: • Influence diffusion models – Influence diffusion models measure the influence of users through their ability to spread information [16]. • Centrality measures – Centrality measures classify users according to their position on the network. Centrality measures the central position and importance of a user in a social network [16]. 7 • Influence measures based on walks between pair of users – These types of measures provide relative power or status of user in a network by accounting all length paths between pair of nodes [26]. • Link topological ranking measures – According to [8], most centrality metrics do not consider the variation of nodes in their calculation: these metrics consider that all nodes contribute equally to their calculation. However, different types of nodes execute an important role in social networks. • Types of influence maximization algorithm – Maximizing influence is a problem widely studied by the community. Influence maximization algorithms should perform fast calculations, high accuracy, and low storage capacity [15]. • Others – This category includes measures used by social networks such as Twitter to measure the influence of users [27]. 4.2 Metrics and algorithms overview In the category of Influence diffusion models we found the following models: Linear threshold model (LT model), Independent cascade model (IC model), Heat diffusion model (HD model), and Epidemic models (Table 2). To apply the LT model and IC model, it is necessary to perform the Monte Carlo simulation to determine the influence of a node for a given period. However, the Monte Carlo simulation is time-consuming and inadequate for large-scale social networks [15]. The IC model is used to find highly influential users, find the maximum influence, predict the development of cascades, and understand the diffusion structure in the networks [20], [28]. Similar to the IC model, the LT model is mainly used to maximize the influence of propagation on the network. Epidemic models are used to find the source of the viral disease and to find the sources of rumours. The epidemic disease in the population is similar to the spread of rumours on a social network [8], [28]. However, these models ignore the topological characteristics of social networks [15]. Table 2. Influence diffusion models. Influence diffusion models Description LT model In this model, a new idea, or innovation is adopted by a user u, only when a certain number of users influence that user u [8]. In a social network G=(V,E), the sum of the influence weights of all neighbouring nodes of node vi corresponds to: ∑ 𝑤𝑖𝑗 ≤1 𝑣𝑗∈𝑁𝑔𝑖𝑎𝑐𝑡 , where 𝑤𝑖𝑗 corresponds to influence weights between node vi and its neighbour node vj, and 𝑁𝑔𝑖𝑎𝑐𝑡 corresponds to the neighbouring nodes activated by node vi [15]. IC model The IC model describes the procedure of influence propagation in a probabilistic way: a user can influence (activate) his neighbour with a certain probability [8], [16]. The IC model is represented as follows [20]: • The initial seed set creates the active sets St for all t≥1 using the following rule: at each phase t≥1, the first activation step is considered from the set St para St-1; then, for each inactive node u, an activation attempt is performed using the Bernoulli test with a probability of success p(u,v). 8 Influence diffusion models Description HD model There is a similarity between the heat diffusion and the information spread on social networks: a user selecting information acts as a source of heat, which diffuses his influence on the social network [8], [15]. Epidemic models Epidemic models correspond to models capable of studying the influence of a macroscopic perspective [8]. According to [29], epidemic models are classified into three categories: deterministic models, stochastic models, and space-time models. • Deterministic models include the susceptible-infectious model (SI model), the susceptible-infectious-susceptible model (SIS model), and the susceptible-infectious-recovery model (SIR model). • The stochastic epidemic model includes the discrete-time, continuous-time Markov model, and the stochastic differential equation model. • The space-time models introduce automated cell phones to model the spread of influence. In the category of Centrality measures we found the following metrics: degree centrality, closeness centrality, betweenness centrality and, eigenvector centrality (Table 3). Centrality metrics measure a user position in a social network, and the most used tools are graph theory and network analysis [8]. These metrics are used to find the most central and influential node in the network. The centrality metrics for finding the centrality of the node depend on the structural properties of the network and make use of flows to analyse these characteristics [16], [26], [28]. Table 3. Centrality Measures. Centrality Measures Description Degree centrality In a social network G=(V,E), degree centrality metric correspond to the number of neighbours of a node, that is, the number of edges that a node has [30]–[33]. It is usually calculated by dividing the degree of a node (ki) by N-1, restricting the value in the range of [0,1]. The equation that defines it is as follows: 𝐶𝐷(𝑖)=𝑘𝑖 𝑁−1. Closeness centrality In a social network G=(V,E), closeness centrality corresponds to the average length of the shortest path from one node to all other nodes [30]–[33]. In the influence analysis, this metric measures the efficiency of each node to disseminate information on the network. [8]. The equation that defines it is as follows: 𝐶𝐶(𝑖)=𝑁−1 ∑𝑑𝑖𝑗 𝑁 𝑗≠𝑖 , Where, N is the number of nodes in the network and 𝑑𝑖𝑗 is the distance between node i and node j. Betweenness centrality In a social network G=(V,E), betweenness centrality describes the extent of nodes that need to be crossed to influence other nodes [31]–[33]. The equation that defines it is as follows: 𝐶𝐵(𝑖)= ∑ 𝜎𝑠𝑡(𝑖) 𝜎𝑠𝑡 𝑠≠𝑖≠𝑡∈𝑉,𝑠<𝑡 , Where 𝜎𝑠𝑡(𝑖) corresponds to the number of shortest paths between nodes s and t through the node i, and 𝜎𝑠𝑡 corresponds to the number of shortest paths between nodes s and t. Eigenvector centrality In a social network G=(V,E), eigenvector centrality provides the relative scores for all nodes, according to the nodes connected to the highest scores contribute more to the scores of the nodes than to the lowest scores [32]. Eigenvector centrality use the adjacency matrix, given by: 𝐶𝐸(𝑖)=1 𝜆∑𝐴𝑖𝑗𝐶𝐸(𝑗) 𝑗, Where, 𝐴𝑖𝑗 corresponds ith eigenvector of the adjacency matrix in the network. 9 In the category of Influence measures based on walks between pair of users we found the following metrics: Katz centrality, Hubbel measure, and Bonacich Power Measure (Table 4). The Katz centrality can be used to compute centrality in directed networks (citation networks, WWW, etc.); it can also be used estimate the relative status or influence of user in a social network [8], [20], [34]. Hubbel Measure and Bonacich Power Measure are measures similar to Katz centrality. Table 4. Influence measures based on walks between pair of users. Influence measures based on walks between pair of users Description Katz centrality Katz centrality allows not only direct links received by a user but also popularity or status of users sending links to him to be included in his score. Further, the status of each, who has link with these users in turn, should also be used for calculating scores in social network [26]. The equation that defines it is as follows: 𝐶𝐾𝑎𝑡𝑧 =((𝐼−𝛼𝐴𝑇)−1−𝐼)𝐼, Where, I is the identity matrix, 𝐼 is a vector of size n (n is the number of nodes) consisting of ones. 𝐴𝑇 denotes the transposed matrix of A and (𝐼−𝛼𝐴𝑇)−1 denotes matrix inversion of the term (𝐼−𝛼𝐴𝑇). Through Katz measure, most influential node or individual positive tie network can be found who has connections with most of the other users and can influence or affect other users with his decisions or activities [26]. This measure is similar to PageRank algorithm and eigenvector centrality. Hubbel Measure Hubbel measure corresponds to the flow of influence through interpersonal links in social networks as input and output channels. The Hubbel measure has structural as well as functional significance. The structural significance of index is in identifying cliques and functional significance is in computation of status [26]. This measure is similar to Katz centrality, the Katz measure uses an identity matrix (each node is connected to itself) while the Hubble measure does not. Bonacich Power Measure In social networks, the most central user is not always the most powerful one. In order to distinguish between power and centrality, was proposed a set of measures given by c(α,β). The parameter β is used to reflect the degree and direction (positive or negative) in which individual user status depends upon status of other users in network [26]. Bonacich power measure is useful in valued and signed graphs, negative ties and positive ties networks. In the category of Link topology ranking measures, were found the following metrics: Hyperlink-Induced Topic Search (HITS) algorithm and PageRank Algorithm (Table 5). Except for eigenvector centrality, most centrality metrics do not consider the variation of the nodes, which means that they consider that all nodes contribute equally to the measures [8]. However, the types of nodes execute an important role in social networks. The HITS algorithm aims to classify web pages based on links, while in PageRank all hyperlinked pages receive numerical weights, used to measure the importance of web pages [27]. The HITS algorithm is used to classify publications in citations networks by Citeseer (search engine). In the context of citation networks, it is natural to identify topical reviews as hubs, as they contain many references to influential articles in the literature [34]. 16 References 1. M. Newman, D. J. Watts, and A.-L. Barabási, The Structure and Dynamics of Networks. Princeton University Press, 2006. 2. A. Wright, Glut: Mastering Information Through The Ages. Ithaca, United States: Cornell University Press, 2008. 3. C. Castellano, S. 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