Target set selection in plane graphs

Most research on social networks is concerned with information transmission per se Our aim here is to supplement the social network perspective by incorporating mechanisms that govern social influence Research in social psychology suggests that individuals interact, in large part, to construct a shared reality that consists not only of shared information but also of agreed upon opinions. In this process, they do not simply transmit information, but more importantly, they influence one another to arrive at a common interpretation of information. We will discuss similarities and differences in how networks structure shapes the spread of information and governs social influence. Both simulation and empirical data concerning these two processes show that they operate in a very different way. The spread of information, described as a contagion process describes how individuals learn about new facts. Social influence process describes how individuals evaluate and weight different items of information and how they change their opinions and attitudes. The results of numerous experiments have shown that three critical factors determine the impact of social influence: (1) the number of sources exerting the influence, (2) the immediacy of the source(s) to the target(s), and (3) the strength of the source(s). The process by which humans construct social reality may prove informative for designing rules of interaction among intelligent agents. The primary implication of the present model is that information is not merely acquired, but also evaluated and negotiated in a social context. The process by which humans evaluate information and construct social reality may prove informative for designing rules of interaction among intelligent agents. The primary implication of the present model is that information is not merely acquired, but also evaluated and negotiated in a social context.

We consider dynamic subgraph connectivity problems for planar undirected graphs. In this model there is a fixed underlying planar graph, where each edge and vertex is either off (failed) or (recovered). We wish to answer connectivity queries with respect to the subgraph. The model has two natural variants, one in which there are d edge/vertex failures that precede all connectivity queries, and one in which failures/recoveries and queries are intermixed. We present a d-failure connectivity oracle for planar graphs that processes any d edge/vertex failures in sort(d,n) time so that connectivity queries can be answered in pred(d,n) time. (Here sort and pred are the time for integer sorting and integer predecessor search over a subset of [n] of size d.) Our algorithm has two discrete parts. The first is an algorithm tailored to triconnected planar graphs. It makes use of Barnette's theorem, which states that every triconnected planar graph contains a degree-3 spanning tree. The second part is a generic reduction from general (planar) graphs to triconnected (planar) graphs. Our algorithm is, moreover, provably optimal. An implication of Pǎtrascu and Thorup's lower bound on predecessor search is that no d-failure connectivity oracle (even on trees) can beat pred(d,n) query time. We extend our algorithms to the subgraph connectivity model where edge/vertex failures (but no recoveries) are intermixed with connectivity queries. In triconnected planar graphs each failure and query is handled in O(logn) time (amortized), whereas in general planar graphs both bounds become O(log2n).

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.

The relationships and interactions between social actors shape the structure and function of social systems. Informal social networks—homogeneous spaces based on shared social and cultural characteristic —play a crucial role in the emergence and persistence of irregular migration, particularly among Georgian migrants in Italy. This study employs a qualitative case study approach focusing on the years 2017–2020. Data were collected through semi-structured interviews with irregular Georgian migrants residing in Italy. Content analysis was applied within the theoretical framework of network theory and symbolic interactionism. The research demonstrates that the idea and practices of irregular migration are primarily generated and transmitted within informal social networks composed of individuals connected by similarities in age, class, and social background. These networks are characterized by tight bonds, mutual trust, and strong norms of reciprocity—often encapsulated in the Georgian idiom, “a hand washes a hand.” The data also support Mark Granovetter’s theory on the strength of weak ties, as the diffusion of diverse and updated information is enabled by more expansive and loosely connected networks (Granovetter, 1973). Such networks serve as vital mechanisms for adaptation and social integration within host countries. In addition, formal institutional supports—such as Georgian Orthodox churches, clergy, and diaspora associations—were found to supplement informal networks in facilitating irregular migration and social support. Informal social networks not only facilitate the decision-making and implementation processes of irregular migration but also create a parallel system of migration management. Their legitimacy and capacity for resource exchange make them a foundational component in sustaining irregular migration as an institutionalized practice.

The analysis of social networks, which focuses on the relationship between social entities today is an area of active research. It is a set of tools for research, in particular, in combination with artificial intelligence methods such as machine learning, deep learning. The paper examined the current quality of the assessment of information in social networks, analyzed the methods of searching and sorting information in various social networks, as well as the process of providing recommendations to users. Social media data is an inexhaustible source of research and business opportunities. In general, social media data is information gathered from social networks that shows how users interact with content. Methods of improving search results for personalizing recommendations in social networks are given. These indicators and statistics provide an effective understanding of the strategy of behavior in social networks. The advantages and disadvantages of a multifactor assessment system are considered. The possible ways of integrating the combined system of evaluating information elements by the user to optimize search queries and filtering big data are identified.

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 networks during the transition to adulthood from the perspective of Israeli care leavers and their social workers

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.

We consider a population of interconnected individuals that, with respect to a piece of information, at each time instant can be subdivided into three (time‐dependent) categories: agnostics, influenced, and evangelists. A dynamical process of information diffusion evolves among the individuals of the population according to the following rules. Initially, all individuals are agnostic. Then, a set of people is chosen from the outside and convinced to start evangelizing, that is, to start spreading the information. When a number of evangelists, greater than a given threshold, communicate with a node v, the node v becomes influenced, whereas, as soon as the individual v is contacted by a sufficiently much larger number of evangelists, it is itself converted into an evangelist and consequently it starts spreading the information. The question is: How to choose a bounded cardinality initial set of evangelists so as to maximize the final number of influenced individuals? We prove that the problem is hard to solve, even in an approximate sense. On the positive side, we present exact polynomial time algorithms for trees and complete graphs. For general graphs, we derive exact parameterized algorithms. We also study the problem when the objective is to select a minimum number of evangelists capable of influencing the whole network. Our motivations to study these problems come from the areas of Viral Marketing and spread of influence in social networks. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 71(4), 346–357 2018

The informal social networks are one of the prominent factors in the labor market decisions both for the supply and demand side. Particularly, in developing countries, like Turkey, these informal networks have an influence on the labor market. However, even the existence of this issue, the impact of informal social networks has not been argued sufficiently for the Turkish case. In this respect, this study advances existing researches, by implementing the quantile regression method to reveal the impact of the informal social networks. The quantile regression analysis reveals the impacts of the different quantiles of wages. The Household Labor Force Survey (HLFS) is utilized for 2004-2016 period. The findings indicate that being recruited by social contacts has negative impact on wage levels and in consequence, aggregate productivity is decreased from low quality of labor force and the low return to the firm.

The development of the post-industrial society requires the acceleration of the integration of the national economy into the globalized economic space. This stage is characterized by active informatization of all spheres of life in society, which requires information security and cyber protection for high-quality information provision of the country’s population, intellectualization of economic processes and prevention of destructive informational influence on the social status of the individual. It is also necessary to consider that for Ukraine the specified stage is complicated by the hybrid war with Russia, which requires strengthening the protection of information from cyber-attacks and the formation of new approaches in preserving the quality of information on social networks. Therefore, the purpose of this article is the development of scientific and methodological approaches in information security management, strengthening its social significance. This requires solving a certain range of tasks of identifying and preventing socially dangerous information based on the use of economic and mathematical methods and models. The article highlights the main directions of socialization of modern technological development and theoretically substantiates its significant impact on human consciousness and behavior, puts a person in front of serious challenges and, under conditions of hybrid warfare, requires strengthening of information security in social networks. In the work, the components of information security are supplemented, its impact on social aspects of society’s life is highlighted. As a result of the research, the authors proposed a scientific and methodical approach to the construction of a system for countering the spread of socially dangerous information in social networks. Besides, its functional elements are highlighted. A method of combating the spread of harmful information in social networks has been developed, which solves the problem of information support of the decision-making process and includes providing the chosen and alternative options to the person making the decision, with the justification of the choice. This creates prerequisites for information support for making a well-founded management decision.

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.

<span lang="EN-US">Social networks provide a fairly wide range of data that allows one way or another to evaluate the effect of the dissemination of information. This article presents the results of a study that describes methods for determining the key parameters of the model needed to analyze and predict the dissemination of information in social networks. An approach based on the analysis of statistical data on user behavior in social networks is proposed. The process of evaluating the main features of the model is described, including the mathematical methods used for data analysis and information dissemination modeling. The study aims to understand the processes of information dissemination in social networks and develop recommendations for the effective use of social networks as a communication and brand promotion tool, as well as to consider the analytical properties of the classical susceptible-infected-removed (SIR) model and evaluate its applicability to the problem of information dissemination. The results of the study can be used to create algorithms and techniques that will effectively manage the process of information dissemination in social networks.</span>

The computation of a group Steiner tree (GST) in various types of graph networks, such as social network and transportation network, is a fundamental graph problem in graphs, with important applications. In these graphs, time is a common and necessary dimension, for example, time information in social network can be the time when a user sends a message to another user. Graphs with time information can be called temporal graphs. However, few studies have been conducted on GST in terms of temporal graphs. This study analyzes the computation of GST for temporal graphs, i.e., the computation of temporal GST (TGST), which is shown to be an NP‐hard problem. We propose an efficient solution based on a dynamic programming algorithm for our problem. This study adopts new optimization techniques, including graph simplification, state pruning, and A∗ search, are adopted to dramatically reduce the algorithm search space. Moreover, we consider three extensions for our problem, namely the TGST with unspecified tree root, the progressive search of TGST, and the top‐N search of TGST. Results of the experimental study performed on real temporal networks verify the efficiency and effectiveness of our algorithms.

On external-memory MST, SSSP and multi-way planar graph separation