Evangelism in social networks: Algorithms and complexity

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model agents change behaviors/opinions on the basis of information collected from their neighbors in a time interval of bounded size whereas agents are assumed to have unbounded memory in previously studied scenarios. In our mathematical framework, one is given a network G = (V,E), an integer value t(v) for each node v ∈ V, and a time window size λ. The goal is to determine a small set of nodes (target set) that influences the whole graph. The spread of influence proceeds in rounds as follows: initially all nodes in the target set are influenced; subsequently, in each round, any uninfluenced node v becomes influenced if the number of its neighbors that have been influenced in the previous λ rounds is greater than or equal to t(v). We prove that the problem of finding a minimum cardinality target set that influences the whole network G is hard to approximate within a polylogarithmic factor. On the positive side, we design exact polynomial time algorithms for paths, rings, trees, and complete graphs.

For businesses, discovering key nodes in social networks has a high computational overhead and cost. Because of this, in the problem of influence maximization, at least key nodes with the most influence in social networks are chosen at the lowest possible cost. Numerous algorithms have been proposed to find key nodes in social networks using the technique of influence maximization under the characteristics of submodularity and monotonicity; however, these algorithms struggle with the issue of optimal influence spread because some graph characteristics are ignored when considering diffusion and influence spread in the social network. The HSMD method, which gives special weight to the structure of communities and selects key nodes hierarchically utilizing the structure of communities, has been presented as a solution to this challenge. Based on the characteristics and strategic placement of the nodes within each community, weight is given to each community in this algorithm. Seed nodes are then chosen hierarchically using BFS traversal. This method enhanced the influence spread rate and execution time of recently introduced algorithms such as CTIM, IMBC, RNR, HEDVGreedy, and k-shell.

Modeling the spread of influence in online social networks is important for predicting the influence of individualsand better understanding many scenarios in social networks, such as the influence maximization problem. The previous work on modeling the spread of influence makes the assumption that the statuses of nodes in a network are independent of each other,which is apparently not correct for social networks. The goal of this work is to derive an accurate mathematical model to characterize the spread of influence for the independent cascade diffusion process in online social networks. Specifically, we apply the susceptible-infected-recovered epidemic model from epidemiology to characterize the independent cascade diffusion processand derive a general mathematical framework. To approximate the complex spatial dependence among nodes in a network, we propose a Markov model to predict the spread of influence. Through the extensive simulation study over several generated topologies and a real coauthorship network,we show that our designed Markov model has much better performance than the existing independent model in predicting the influence of individuals in online social networks.

The spread of influence in a network is a fundamental issue in many complex systems. For instance, the word of-mouth effect in a social network is crucial to the emerging viral market. The process was previously analyzed with a voter model where an individual weighs the opinions of his acquaintances equally. However, one would expect that an individual's opinion is often more swayed by her/his better connected peers. As such, the influence of a node x on another node should be proportional to x's degree. This paper studies the spread of influence under the latter model - called Preferential Voter Model (PVM) for easier reference. We first present the exact form of the random walk stationary distribution for PVM, based on which, we show that the First Passage Time (FPT) of PVM follows an exponential decay. Furthermore, compared against the conventional (nonpreferential) voter model, we show that nodes with larger degrees exhibit faster decay rate and lower mean First Passage Time in PVM. These new results have applications to network-based complex systems. For instance, in the context of viral marketing in a social network, picking nodes of larger degrees as the starting nodes of a sales campaign not only maximizes the expected number of influenced nodes in the network, but also reduces the expected time to spread the influence. Thus, our result confirms analytically that well-connected individuals indeed exert faster and more effective influences in social networks under the preferential model.

Social Network Influences on Service Use Among Urban, African American Youth with Mental Health Problems

The target set selection (TSS) problem was initially proposed to study the spread of information, ideas, or influence in social networks. It has been used to model many problems arising in various practical applications. In this paper, we study the TSS problem for plane graphs. We provide a characterization of plane graphs $ G $ for which $ \min_3(G) = 3 $. Consequently, we show that the minimum degree of such plane graphs is at most 4.

Understanding how information flows in online social networks is of great importance. It is generally difficult to obtain accurate prediction results of cascades over such networks, therefore a variety of diffusion models have been proposed in the literature to simulate diffusion processes instead. We argue that such models require extensive simulation results to produce good estimates of future spreads. In this work, we take a complimentary approach. We present a generalized, analytical model of influence in social networks that captures social influence at various levels of granularity, ranging from pairwise influence, to local neighborhood, to the general population, and external events, therefore capturing the complex dynamics of human behavior. We demonstrate that our model can integrate a variety of diffusion models. Particularly, we show that commonly used diffusion models in social networks can be reduced to special cases of our model, by carefully defining their parameters. Our goal is to provide a closed-form expression to approximate the probability of infection for every node in an arbitrary, directed network at any time t. We quantitatively evaluate the approximation quality of our analytical solution as compared to numerous popular diffusion models on a real-world dataset and a series of synthetic graphs.

Influence models enable the modelling of the spread of ideas, opinions and behaviours in social networks. Bounded rationality in social networks suggests that players make non-optimum decisions due to the limitations of access to information. Based on the premise that adopting a state or an idea can be regarded as being ‘rational’, we propose an influence model based on the heterogeneous bounded rationality of players in a social network. We employ the quantal response equilibrium model to incorporate the bounded rationality in the context of social influence. We hypothesise that bounded rationality of following a seed or adopting the strategy of a seed is negatively proportional to the distance from that node, and it follows that closeness centrality is the appropriate measure to place influencers in a social network. We argue that this model can be used in scenarios where there are multiple types of influencers and varying pay-offs of adopting a state. We compare different seed placement mechanisms to compare and contrast the optimum method to minimise the existing social influence in a network when there are multiple and conflicting seeds. We ascertain that placing of opposing seeds according to a measure derived from a combination of the betweenness centrality values from the seeds, and the closeness centrality of the network provide the maximum negative influence. Further, we extend this model to a strategic decision-making scenario where each seed operates a strategy in a strategic game.

Relevance of the topic. Today, the role of marketing is to satisfy the consumer's curiosity through transparent and valuable content (Sawicki, 2016). More than 4 billion people around the world regularly use online services to find their products, entertainment, friends and even romances, and the behavior of customers and the way companies sell their products to both consumers and businesses has changed a lot (Chaffey & Ellis-Chadwick, 2019). As the use of the Internet has grown, so have related activities such as digital marketing. The main difference between traditional and digital marketing is that digital marketing focuses on the customer, offering him a personal message and a response to his request (Ištvanić, Crnjac Milić & Krpić, 2017). Digital marketing is an integral part of the digital business transformation process. It includes new marketing methods based on information and communication technologies. Todor (2015) the study is based on a study by ZenitOptimedia, which shows that internet use has increased significantly over the past five years, while the use of other media has decreased or only slightly increased. The situation is as follows: internet (+105 %.), outdoor advertising (+3%), television (-8%), cinema (-11%), radio (-15%), magazines (-23%), newspapers (-31%). For this reason, its application in practice is a prerequisite for the successful development of business in modern market conditions (Veleva & Tsvetanova, 2020).
 The problem. Football fans around the world are increasingly communicating with each other on social networks (Parganas et al., 2017), and football clubs, regardless of their degree of professionalism, include a large number of social media/media platforms for their online campaigns (Helleu, 2017). Bagchi, Sreepada (2020) in the survey conducted, respondents expressed their opinion about the social networks of their favorite football club and why they follow the news of the club in them. Especially during the COVID-19 pandemic, the influence of social networks on football has increased. The clubs tried to give interesting and new content to the fans. Some organized social media quizzes, others made videos with a message that the stadium missed the fans (Szczepkowski, 2021).
 The aim of the study is to analyze the influence of digital marketing on the communication of football clubs in the case of Lithuania.
 The subject of the study is the influence of digital marketing on the communication of football clubs.
 The choice of assessing the influence of electronic marketing on the communication of football clubs was determined by the popularity of the sport in the world, the constantly growing sports market and a large fan base. The quantitative research method chosen for the survey is a questionnaire survey. The quantitative study examined the opinions and behavior of fans of Lithuanian football clubs – consumers – related to the applied online marketing tools. In order to assess the influence of digital marketing on the communication of football clubs, literary analysis and empirical research were chosen. The questionnaire was compiled on the basis of Vale & Fernandes (2018) “Social media and sports: driving fan engagement with football clubs on Facebook” research. To obtain a targeted sample of those who responded in the study, paniotto's sample size formula (Bokor et al., 2011) was used to avoid going beyond the 5 percent error. A total of 451 respondents participated in the survey.
 Results and conclusion. The largest part of football clubs follow with the help of social networks and even note that they monitor the news on a daily basis thanks to social media platforms. All categories of questions were dominated by the influence of social networks on the communication of the football club. From the results of the study, it is noted that clubs use various strategies, but dominate and fans like social networks the most. Their rating from the presented means was the best. In addition, the respondents were quite unanimous in answering the questions of involvement in the activities of the community - they agree that the activities of the supported football club are important to them. The vast majority of the study participants are happy to get involved in the activities of the communities of clubs and organizations, which give them good emotions, relax them, help them escape from the routine and reduce the feeling of loneliness. The vast majority emphasize that they see basic information about the activities of the clubs there. Also on the Internet buys club products (tickets, merchandise), which also shows that digitalization has progressed in the football world. In conclusion, it can be noted that social networks dominated throughout the study, both on the part of football organizations – communication is developed thanks to this tool and from the part of fans – they recognize it as the most effective tool.
 Keywords: digital marketing in football, football club communication, A League

The evolution of influencer marketing relies on a social phenomenon, i.e., influence diffusion. The modelling and analysis of influence propagation in social networks has been extensively investigated by both researchers and practitioners. Nearly all of the works in this field assume influence is driven by a single factor, e.g., friendship affiliation. However, influence spread through many other pathways, such as face-to-face interactions, phone calls, emails, or even through the reviews posted on web-pages. In this paper, we modelled the influence-diffusion space as a hybrid social network, where both direct and indirect influence are considered. Furthermore, a concrete implementation of hybrid social network, i.e., Comprehensive Influence Propagation model is articulated. The proposed model can be applied as an effective approach to tackle the multi-faceted influence diffusion problems in social networks. We also evaluated the proposed model in the influence maximization problem in different scenarios. Experimental results reveal that the proposed model can perform better than those considering a single aspect of influence.

Over the past 20 years, researchers have shown increasing interest in social network analysis to understand second language acquisition (SLA), especially in a study abroad (SA) context. To date, few longitudinal studies have examined the joint evolution of the learners’ sociolinguistic competence and socialisation during the SA. By shifting the focus from a global view of the study abroad context to a deep analysis of the composition and structure of each learner’ social networks in the host country, we aim to provide a better understanding of the development of sociolinguistic competence in SLA (Gautier & Chevrot, 2015). We apply the sociological concept of a social network to sociolinguistics. To explore the sociolinguistic competence of 29 learners, we focus on two well-described sociolinguistic variables in French: the optional liaison and the negative ne. We also gathered data on their social networks and provided a deep analysis of each participant’s network. We implemented a quantitative approach to analyse and depict the social networks of the learners. Statistically significant relationships were found between changes in the learners’ personal network and their use of the two sociolinguistic variables. The development of L2-oriented social networks (in terms of size, speaking time, and frequency) over nine months of the SA helps learners to reduce their use of standard variants. Conversely, the development of L1-oriented social networks during the SA is associated with greater use of standard variants.

The article describes computational experiment and further research work in the area of identification of destructive information influence in social networks. The problem of distribution of suicidal content via open sources is presented. On the basis of calculations there was made a conclusions about the prospects of using the methods of information retrieval in the task of identification of the destructive informational influence. The procedure of singular value decomposition of the matrix pattern-message is considered as a path of the future research.

Influence Maximization aims to find the top-K influential individuals to maximize the influence spread within a social network, which remains an important yet challenging problem. Most existing greedy algorithms mainly focus on computing the exact influence spread, leading to low computational efficiency and limiting their application to real-world social networks. While in this paper we show that through supervised sampling, we can efficiently estimate the influence spread at only negligible cost of precision, thus significantly reducing the execution time. Motivated by this, we propose ESMCE, a power-law exponent supervised Monte Carlo estimation method. In particular, ESMCE exploits the power-law exponent of the social network to guide the sampling, and employs multiple iterative steps to guarantee the estimation accuracy. Moreover, ESMCE shows excellent scalability and well suits large-scale social networks. Extensive experiments on six real-world social networks demonstrate that, compared with state-of-the-art greedy algorithms, ESMCE is able to achieve almost two orders of magnitude speedup in execution time with only negligible error (2.21 % on average) in influence spread.

Foreign language communication as a modern value is substantiated in the article. The author describes decisive role of social networks as a revolutionary tool for interpersonal interaction as well as a platform for learning foreign languages. The influence of social networks on various aspects of human life is revealed in the article. The purpose of the paper is to find effective strategies for learning foreign languages using social networks and multilingual resources. Basic scientific methods applied are: analysis,synthesis and comparison. The reasons of social networks popularity as a tool that modified the format of communicationare revealed. The author suggests considering the role of social networks for formal, informal and selfeducation. The article does not provide an exhaustive list of advantages and disadvantages of using social networks for educational purposes. A comparative analysis conducted in the study allows students to focus on the strong points of new technologies and comprehend fully difficulties and challenges caused by an active use of social networks during learning. The author emphasizes the importance of psychologicalcomfort in social networks and the differences that exist between real and virtual worlds, where a person can design a desired model of his own life, often imaginary. Ways of using multilingual social networks for learning foreign languages are analyzed in thearticle. The material in the table reveals the level that one can achieve in case of self-education using social networks. The author suggests considering social networks as a modern way of making the study of foreign languages fascinating and interesting. The arguments for using various electronic programs on paid basis are given and grounded.The author gives recommendations on studying foreign languages. The article highlights how important it is to define goals and choose the right learning strategy and emphasizes on the need to expand constantly learner’s own vocabulary. To accelerate the development of necessary linguistic skills and enhance motivation to study the author encourages using additional resources.

Influence maximization, defined as finding a small subset of nodes that maximizes spread of influence in social networks, is NP-hard under both Independent Cascade (IC) and Linear Threshold (LT) models, where many greedy-based algorithms have been proposed with the best approximation guarantee. However, existing greedy-based algorithms are inefficient on large networks, as it demands heavy Monte-Carlo simulations of the spread functions for each node at the initial step [7] . In this paper, we establish new upper bounds to significantly reduce the number of Monte-Carlo simulations in greedy-based algorithms, especially at the initial step. We theoretically prove that the bound is tight and convergent when the summation of weights towards (or from) each node is less than 1. Based on the bound, we propose a new Upper Bound based Lazy Forward algorithm ( UBLF in short) for discovering the top-k influential nodes in social networks. We test and compare UBLF with prior greedy algorithms, especially CELF [30] . Experimental results show that UBLF reduces more than 95 percent Monte-Carlo simulations of CELF and achieves about $2\hbox{-}10$ times speedup when the seed set is small.