Analyzing the Growth of Social Networks Using Quadratic Functions to Model the Spread of Information and Influence

With the rise of social networks the ways in which consumers communicate have changed sustainably. Companies recognise this change, and use word-of-mouth communication and viral marketing as means to reflect this change and to communicate with consumers and attract their attention. This is particularly true for the music business, where viral marketing is important. However, at the same time knowledge is missing regarding the systematic conduction of viral marketing in social networks, especially for music. Therefore, in this paper it is analysed (1) how the characteristics of digital music affect the viral marketing process, (2) critical factors for the viral marketing of digital music are derived and (3) the factors are evaluated in qualitative interviews. Thereby this paper (1) contributes to the understanding of how social networks can be used for viral marketing activities and (2) provides a scientific foundation and practical guiding points for the systematic undertaking of viral marketing of digital music in social networks. The findings are important for the emerging area of research on viral music marketing and for the challenges of music marketers in practice.

Signaling and Reciprocity

Evaluating influence spread in social networks is a fundamental procedure to estimate the word-of-mouth effect in viral marketing. There are enormous studies about this topic; however, under the standard stochastic cascade models, the exact computation of influence spread is known to be #P-hard. Thus, the existing studies have used Monte-Carlo simulation-based approximations to avoid exact computation. We propose the first algorithm to compute influence spread exactly under the independent cascade model. The algorithm first constructs binary decision diagrams (BDDs) for all possible realizations of influence spread, then computes influence spread by dynamic programming on the constructed BDDs. To construct the BDDs efficiently, we designed a new frontier-based search-type procedure. The constructed BDDs can also be used to solve other influence-spread related problems, such as random sampling without rejection, conditional influence spread evaluation, dynamic probability update, and gradient computation for probability optimization problems. We conducted computational experiments to evaluate the proposed algorithm. The algorithm successfully computed influence spread on real-world networks with a hundred edges in a reasonable time, which is quite impossible by the naive algorithm. We also conducted an experiment to evaluate the accuracy of the Monte-Carlo simulation-based approximation by comparing exact influence spread obtained by the proposed algorithm.

Influence maximization, whose objective is to select k users (called seeds) from a social network such that the number of users influenced by the seeds (called influence spread) is maximized, has attracted significant attention due to its widespread applications, such as viral marketing and rumor control. However, in real-world social networks, users have their own interests (which can be represented as topics) and are more likely to be influenced by their friends (or friends' friends) with similar topics. We can increase the influence spread by taking into consideration topics. To address this problem, we study topic-aware influence maximization, which, given a topic-aware influence maximization (TIM) query, finds k seeds from a social network such that the topic-aware influence spread of the k seeds is maximized. Our goal is to enable online TIM queries. Since the topic-aware influence maximization problem is NP-hard, we focus on devising efficient algorithms to achieve instant performance while keeping a high influence spread. We utilize a maximum influence arborescence (MIA) model to approximate the computation of influence spread. To efficiently find k seeds under the MIA model, we first propose a best-effort algorithm with 1 − 1/ e approximation ratio, which estimates an upper bound of the topic-aware influence of each user and utilizes the bound to prune large numbers of users with small influence. We devise effective techniques to estimate tighter upper bounds. We then propose a faster topic-sample-based algorithm with ε · (1 − 1/ e ) approximation ratio for any ε ∈ (0, 1], which materializes the influence spread of some topic-distribution samples and utilizes the materialized information to avoid computing the actual influence of users with small influences. Experimental results show that our methods significantly outperform baseline approaches.

Influence maximization is a problem of finding a small set of highly influential individuals in social networks to maximize the spread of influence. However, the distinction between the spread of influence and profit is neglected. The problem of profit maximization in social network extends the influence maximization problems to a realistic setting aiming to gain maximum profit in social networks. In this paper, we consider how to sell the digital goods (near zero marginal cost) by viral marketing in social network. The question can be modeled as a profit maximization problem. We show the problem is an unconstrained submodular maximization and adopt two efficient algorithms from two approaches. One is a famous algorithm from theoretical computer science and that can achieve a tight linear time (1/2) approximation. The second is to propose a profit discount heuristic which improves the efficiency. Through our extensive experiments, we demonstrate the efficiency and quality of the algorithms we applied. Based on results of our research, we also provide some advice for practical viral marketing.

Identifying influencers in a given social network has become an important research problem for various applications, including accelerating the spread of information in viral marketing and preventing the spread of fake news and rumors. The literature contains a rich body of studies on identifying influential source spreaders who can spread their own messages to many other nodes. In contrast, the identification of influential brokers who can spread other nodes' messages to many nodes has not been fully explored. Theoretical and empirical studies suggest that involvement of both influential source spreaders and brokers is a key to facilitating large-scale information diffusion cascades. Therefore, this paper explores ways to identify influential brokers from a given social network. By using three social media datasets, we investigate the characteristics of influential brokers by comparing them with influential source spreaders and central nodes obtained from centrality measures. Our results show that (i) most of the influential source spreaders are not influential brokers (and vice versa) and (ii) the overlap between central nodes and influential brokers is small (less than 15%) in Twitter datasets. We also tackle the problem of identifying influential brokers from centrality measures and node embeddings, and we examine the effectiveness of social network features in the broker identification task. Our results show that (iii) although a single centrality measure cannot characterize influential brokers well, prediction models using node embedding features achieve F1 scores of 0.35--0.68, suggesting the effectiveness of social network features for identifying influential brokers.

Maximizing influence under influence loss constraint in social networks

Influence maximization is a fundamental research problem in social networks. Viral marketing, one of its applications, is to get a small number of users to adopt a product, which subsequently triggers a large cascade of further adoptions by utilizing “Word-of-Mouth” effect in social networks. Time plays an important role in the influence spread from one user to another and the time needed for a user to influence another varies. In this paper, we propose the time constrained influence maximization problem. We show that the problem is NP-hard, and prove the monotonicity and submodularity of the time constrained influence spread function. Based on this, we develop a greedy algorithm. To improve the algorithm scalability, we propose the concept of Influence Spreading Path in social networks and develop a set of new algorithms for the time constrained influence maximization problem. We further parallelize the algorithms for achieving more time savings. Additionally, we generalize the proposed algorithms for the conventional influence maximization problem without time constraints. All of the algorithms are evaluated over four public available datasets. The experimental results demonstrate the efficiency and effectiveness of the algorithms for both conventional influence maximization problem and its time constrained version.

Our study concerns an important current problem, that of influence maximization in social network. This problem has received significant attention from the researchers recently, driven by many potential applications such as viral marketing and sales promotion. It is a fundamental issue to find a subset of key individuals in a social network such that targeting them initially (e.g. to adopt a new product) will maximize the spread of the influence (further adoptions of the new product). However, the problem of finding the most key nodes is unfortunately NP-hard. It has been shown that a greedy algorithm with provable approximation guarantees can give good approximation. However, it is computationally expensive, if not prohibitive, to run the greedy algorithm on a large social network. Based on the community structure property of social network, a cooperative game theoretic algorithm CGINA to find key nodes is proposed. The proposed algorithm encompasses two stages. Firstly, we detect the community structure of the social network with the topological structure and information diffusion model. In this paper, we adopt the algorithm 2 in [4]. Then, we will find key nodes in communities. In this paper, we think of the information diffusion in the whole network as a cooperative game with transferable utility. The communities of the network happen to be the players in this cooperative game. With the solution concept Shapley value in game theory, we allocate the number of key nodes to discover in the community. Moreover, different from the existing relevant literature, in my opinion, the key nodes two parts. One is composed of “bridge” nodes, which contact other communities densely, and are easy to disseminate information across communities, the other is composed of “influential” nodes, which are at the core of the community, in close touch with other nodes, and can diffuse information quickly within the community. To adjust the ratio of these two kinds of nodes in the same community, a heuristic factor l is introduced. Empirical studies on a large social network show that our algorithm is efficient and powerful.

Word-of-mouth plays an important role in the spread of influence by means of a cascading manner, e.g., the promotion of new products, information dissemination, etc. Today’s Online Social Networks (OSNs) provide viral marketing for many companies to conduct business promotion, and the idea behind viral marketing comes from the word-of-mouth effects. Given a predefined budget (e.g., the set size k), influence maximization selects a set of initial users to help companies to promote their products. The budget-making often is of challenging owning to the hardness of trade-off between profit and cost. Most of recent research on influence maximization primarily study the problem of independent product promotion, but few take into account the impacts of other existing products that users have already owned. Moreover, the current solutions encounter scalability problem whenever facing a large scale social network. In this paper, we explore the viral marketing by defining a general influence maximization problem where a practical scenario of coexistence of multiple products is considered. To capture the impacts of other existing products, we put forward a new method to measure the influence between users. Different from previous work, the goal of our general problem is to maximize the profit/cost ratio which can avoid the difficulty of budget-making and reflects maximization effects better. Then, we propose a ($\frac {1}{2} + \varepsilon $)-approximate algorithm with linear complexity to solve the problem, and further design a distributed implementation to achieve good scalability. Extensive experiments on real world datasets validate the effectiveness and efficiency of our solution.

Influence maximization in social networks is the problem of finding a set of seed nodes in the network that maximizes the spread of influence under certain information prorogation model, which has become an important topic in social network analysis. In this paper, we show that conventional influence maximization algorithms cause uneven spread of influence among different attribute groups in social networks, which could lead to severer bias in public opinion dissemination and viral marketing. We formulate the balanced influence maximization problem to address the trade-off between influence maximization and attribute balance, and propose a sampling based solution to solve the problem efficiently. To avoid full network exploration, we first propose an attribute-based (AB) sampling method to sample attributed social networks with respect to preserving network structural properties and attribute proportion among user groups. Then we propose an attributed-based reverse influence sampling (AB-RIS) algorithm to select seed nodes from the sampled graph. The proposed AB-RIS algorithm runs efficiently with guaranteed accuracy, and achieves the trade-off between influence maximization and attribute balance. Extensive experiments based on four real-world social network datasets show that AB-RIS significantly outperforms the state-of-the-art approaches in balanced influence maximization.

Influence maximization, fundamental for word-of-mouth marketing and viral marketing, aims to find a set of seed nodes maximizing influence spread on social network. Early methods mainly fall into two paradigms with certain benefits and drawbacks: (1) Greedy algorithms, selecting seed nodes one by one, give a guaranteed accuracy relying on the accurate approximation of influence spread with high computational cost; (2) Heuristic algorithms, estimating influence spread using efficient heuristics, have low computational cost but unstable accuracy. We first point out that greedy algorithms are essentially finding a self-consistent ranking, where nodes' ranks are consistent with their ranking-based marginal influence spread. This insight motivates us to develop an iterative ranking framework, i.e., IMRank, to efficiently solve influence maximization problem under independent cascade model. Starting from an initial ranking, e.g., one obtained from efficient heuristic algorithm, IMRank finds a self-consistent ranking by reordering nodes iteratively in terms of their ranking-based marginal influence spread computed according to current ranking. We also prove that IMRank definitely converges to a self-consistent ranking starting from any initial ranking. Furthermore, within this framework, a last-to-first allocating strategy and a generalization of this strategy are proposed to improve the efficiency of estimating ranking-based marginal influence spread for a given ranking. In this way, IMRank achieves both remarkable efficiency and high accuracy by leveraging simultaneously the benefits of greedy algorithms and heuristic algorithms. As demonstrated by extensive experiments on large scale real-world social networks, IMRank always achieves high accuracy comparable to greedy algorithms, while the computational cost is reduced dramatically, about 10-100 times faster than other scalable heuristics.

Influence maximization is the problem to identify and find a set of the most influential nodes, whose aggregated influence in the network is maximized. This research is of great application value for advertising, viral marketing and public opinion monitoring. However, we always ignore the tendency of nodes’ behaviors and sentiment in the researches of influence maximization. On general, users’ sentiment determines users behaviors, and users’ behaviors reflect the influence between users in social network. In this paper, we design a training model of sentimental words to expand the existing sentimental dictionary with the marked-comment data set, and propose an influence spread model considering both the tendency of users’ behaviors and sentiment named as BSIS (Behavior and Sentiment Influence Spread) to depict and compute the influence between nodes. We also propose an algorithm for influence maximization named as BS-G (BSIS with Greedy Algorithm) to select the initial node. In the experiments, we use two real social network data sets on the Hadoop and Spark distributed cluster platform for experiments, and the experiment results show that BSIS model and BS-G algorithm on big data platform have better influence spread effects and higher quality of the selection of seed node comparing with the approaches with traditional IC, LT and CDNF models.

Influence maximization (IM) aims to find a subset of k nodes that can maximize the final active node set under an information diffusion model. With the development and popularity of social networks, the IM problem plays an essential role in various applications, such as public opinion analysis, viral marketing, and rumor early warning. However, most of the existing IM solutions have not accessed the risk of negative information from nodes in the future. In reality, a company may face economic loss when negative information breaks out of its spokesman. Therefore, a crisis assessment oriented and topic-based IM problem (TIM-CA) is proposed, which is utilized to model the IM problem by considering the crisis assessment (CA) and topics of users. To solve this problem, we propose a maximum influence arborescence model-based algorithm for TIM-CA, namely, MIA-TIM-CA. The proposed algorithm consists of crisis degree calculation, topic relevance calculation, and influence spread evaluation. More importantly, as for crisis degree calculation, it considers self-, topology-, and topic-based crisis degrees for each node. At the influence spread evaluation stage, MIA-TIM-CA proposes two functions to evaluate the node's importance and node influence spread. Extensive experiments on two real-world social networks demonstrate that our MIA-TIM-CA outperforms all comparison algorithms on influence spread, crisis score, and running time.

Given fixed budgets, companies attempt to obtain maximum coverage on a social network by targeting at influential individuals. This viral marketing is often modeled by the independent cascade model. However, identifying the most influential people by computing influence spread is NP-hard, and various approximate algorithms are developed. In this paper, we emphasize the probabilistic nature of influence propagation. We propose to use exact probabilistic solutions and prove an inclusion-exclusion principle for computing influence spread. Our probabilistic solutions can significantly speed up the computation of influence spread. We also give a probabilistic-additive incremental search strategy to solve the influence maximization problem, i.e., to find a subset of individuals that has the largest influence spread in the end. Experiments on real data sets demonstrated the effectiveness and efficiency of our methods.