Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.

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Maximizing the Spread of Influence through a Social Network

In many real-world situations, different and often opposite opinions, innovations, or products are competing with one another for their social influence in a networked society. In this paper, we study competitive influence propagation in social networks under the competitive linear threshold (CLT) model, an extension to the classic linear threshold model. Under the CLT model, we focus on the problem that one entity tries to block the influence propagation of its competing entity as much as possible by strategically selecting a number of seed nodes that could initiate its own influence propagation. We call this problem the influence blocking maximization (IBM) problem. We prove that the objective function of IBM in the CLT model is submodular, and thus a greedy algorithm could achieve 1 − 1/e approximation ratio. However, the greedy algorithm requires Monte-Carlo simulations of competitive influence propagation, which makes the algorithm not efficient. We design an efficient algorithm CLDAG, which utilizes the properties of the CLT model, to address this issue. We conduct extensive simulations of CLDAG, the greedy algorithm, and other baseline algorithms on real-world and synthetic datasets. Our results show that CLDAG is able to provide best accuracy in par with the greedy algorithm and often better than other algorithms, while it is two orders of magnitude faster than the greedy algorithm.

/pdf/influence-blocking-maximization-in-social-networks-under-the-1424s08phy.pdf

Influence Blocking Maximization in Social Networks under the Competitive Linear Threshold Model.

Influence maximization is the problem of selecting top $k$ seed nodes in a social network to maximize their influence coverage under certain influence diffusion models. In this paper, we propose a novel algorithm IRIE that integrates the advantages of influence ranking (IR) and influence estimation (IE) methods for influence maximization in both the independent cascade (IC) model and its extension IC-N that incorporates negative opinion propagations. Through extensive experiments, we demonstrate that IRIE matches the influence coverage of other algorithms while scales much better than all other algorithms. Moreover IRIE is much more robust and stable than other algorithms both in running time and memory usage for various density of networks and cascade size. It runs up to two orders of magnitude faster than other state-of-the-art algorithms such as PMIA for large networks with tens of millions of nodes and edges, while using only a fraction of memory.

/pdf/irie-scalable-and-robust-influence-maximization-in-social-3rm2a62tkk.pdf

IRIE: Scalable and Robust Influence Maximization in Social Networks

Influence maximization, defined by Kempe et al. (SIGKDD 2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. The scalability of influence maximization is a key factor for enabling prevalent viral marketing in large-scale online social networks. Prior solutions, such as the greedy algorithm of Kempe et al. (SIGKDD 2003) and its improvements are slow and not scalable, while other heuristic algorithms do not provide consistently good performance on influence spreads. In this article, we design a new heuristic algorithm that is easily scalable to millions of nodes and edges in our experiments. Our algorithm has a simple tunable parameter for users to control the balance between the running time and the influence spread of the algorithm. Our results from extensive simulations on several real-world and synthetic networks demonstrate that our algorithm is currently the best scalable solution to the influence maximization problem: (a) our algorithm scales beyond million-sized graphs where the greedy algorithm becomes infeasible, and (b) in all size ranges, our algorithm performs consistently well in influence spread—it is always among the best algorithms, and in most cases it significantly outperforms all other scalable heuristics to as much as 100–260% increase in influence spread.

/pdf/scalable-influence-maximization-for-independent-cascade-3ulbamd7q2.pdf

Scalable influence maximization for independent cascade model in large-scale social networks

Influence maximization is the problem of selecting top $k$ seed nodes in a social network to maximize their influence coverage under certain influence diffusion models. In this paper, we propose a novel algorithm IRIE that integrates a new message passing based influence ranking (IR), and influence estimation (IE) methods for influence maximization in both the independent cascade (IC) model and its extension IC-N that incorporates negative opinion propagations. Through extensive experiments, we demonstrate that IRIE matches the influence coverage of other algorithms while scales much better than all other algorithms. Moreover IRIE is more robust and stable than other algorithms both in running time and memory usage for various density of networks and cascade size. It runs up to two orders of magnitude faster than other state-of-the-art algorithms such as PMIA for large networks with tens of millions of nodes and edges, while using only a fraction of memory comparing with PMIA.

Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. In this paper, we propose an extension to the independent cascade model that incorporates the emergence and propagation of negative opinions. The new model has an explicit parameter called quality factor to model the natural behavior of people turning negative to a product due to product defects. Our model incorporates negativity bias (negative opinions usually dominate over positive opinions) commonly acknowledged in the social psychology literature. The model maintains some nice properties such as submodularity, which allows a greedy approximation algorithm for maximizing positive influence within a ratio of 1-1/e. We define a quality sensitivity ratio (qs-ratio) of influence graphs and show a tight bound of T(vn/k) on the qs-ratio, where n is the number of nodes in the network and k is the number of seeds selected, which indicates that seed selection is sensitive to the quality factor for general graphs. We design an efficient algorithm to compute influence in tree structures, which is nontrivial due to the negativity bias in the model. We use this algorithm as the core to build a heuristic algorithm for influence maximization for general graphs. Through simulations, we show that our heuristic algorithm has matching influence with a standard greedy approximation algorithm while being orders of magnitude faster.

/pdf/influence-maximization-in-social-networks-when-negative-3zt65kr7w2.pdf

Alex Collins

Papers

Influence maximization in social Networks when negative opinions may emerge and propagate