Recently, there has been tremendous interest in the phenomenon of influence propagation in social networks. The studies in this area assume they have as input to their problems a social graph with edges labeled with probabilities of influence between users. However, the question of where these probabilities come from or how they can be computed from real social network data has been largely ignored until now. Thus it is interesting to ask whether from a social graph and a log of actions by its users, one can build models of influence. This is the main problem attacked in this paper. In addition to proposing models and algorithms for learning the model parameters and for testing the learned models to make predictions, we also develop techniques for predicting the time by which a user may be expected to perform an action. We validate our ideas and techniques using the Flickr data set consisting of a social graph with 1.3M nodes, 40M edges, and an action log consisting of 35M tuples referring to 300K distinct actions. Beyond showing that there is genuine influence happening in a real social network, we show that our techniques have excellent prediction performance.

Interaction graphs are ubiquitous in many fields such as bioinformatics, sociology and physical sciences. There have been many studies in the literature targeted at studying and mining these graphs. However, almost all of them have studied these graphs from a static point of view. The study of the evolution of these graphs over time can provide tremendous insight on the behavior of entities, communities and the flow of information among them. In this work, we present an event-based characterization of critical behavioral patterns for temporally varying interaction graphs. We use non-overlapping snapshots of interaction graphs and develop a framework for capturing and identifying interesting events from them. We use these events to characterize complex behavioral patterns of individuals and communities over time. We show how semantic information can be incorporated to reason about community-behavior events. We also demonstrate the application of behavioral patterns for the purposes of modeling evolution, link prediction and influence maximization. Finally, we present a diffusion model for evolving networks, based on our framework.

Influence maximization is the problem of finding a small subset of nodes (seed nodes) in a social network that could maximize the spread of influence. In this paper, we study the efficient influence maximization from two complementary directions. One is to improve the original greedy algorithm of [5] and its improvement [7] to further reduce its running time, and the second is to propose new degree discount heuristics that improves influence spread. We evaluate our algorithms by experiments on two large academic collaboration graphs obtained from the online archival database arXiv.org. Our experimental results show that (a) our improved greedy algorithm achieves better running time comparing with the improvement of [7] with matching influence spread, (b) our degree discount heuristics achieve much better influence spread than classic degree and centrality-based heuristics, and when tuned for a specific influence cascade model, it achieves almost matching influence thread with the greedy algorithm, and more importantly (c) the degree discount heuristics run only in milliseconds while even the improved greedy algorithms run in hours in our experiment graphs with a few tens of thousands of nodes. Based on our results, we believe that fine-tuned heuristics may provide truly scalable solutions to the influence maximization problem with satisfying influence spread and blazingly fast running time. Therefore, contrary to what implied by the conclusion of [5] that traditional heuristics are outperformed by the greedy approximation algorithm, our results shed new lights on the research of heuristic algorithms.

We prove and extend a conjecture of Kempe, Kleinberg, and Tardos (KKT) on the spread of influence in social networks. A social network can be represented by a directed graph where the nodes are individuals and the edges indicate a form of social relationship. A simple way to model the diffusion of ideas, innovative behavior, or “word-of-mouth ” effects on such a graph is to consider an increasing process of “infected” (or active) nodes: each node becomes infected once an activation function of the set of its infected neighbors crosses a certain threshold value. Such a model was introduced by KKT in [7, 8] where the authors also impose several natural assumptions: the threshold values are (uniformly) random to account for our lack of knowledge of the true values; and the activation functions are monotone and submodular, i.e. have “diminishing returns. ” The monotonicity condition indicates that a node is more likely to become active if more of its neighbors are active, while the submodularity condition, indicates that the marginal effect of each neighbor is decreasing when the set of active neighbors increases. For an initial set of active nodes S, let σ(S) denote the expected number of active nodes at termination. Here we prove a conjecture of KKT: we show that the function σ(S) is submodular under

Abstract. Social networks often serve as a medium for the diffusion of ideas or innovations. An individual’s decision whether to adopt a product or innovation will be highly dependent on the choices made by the individual’s peers or neighbors in the social network. In this work, we study the game of innovation diffusion with multiple competing innovations such as when multiple companies market competing products using viral marketing. Our first contribution is a natural and mathematically tractable model for the diffusion of multiple innovations in a network. We give a (1−1/e) approximation algorithm for computing the best response to an opponent’s strategy, and prove that the “price of competition ” of this game is at most 2. We also discuss “first mover ” strategies which try to maximize the expected diffusion against perfect competition. Finally, we give an FPTAS for the problem of maximizing the influence of a single player when the underlying graph is a tree. 1

We consider the problem faced by a company that wants to use viral marketing to introduce a new product into a market where a competing product is already being introduced. We assume that consumers will use only one of the two products and will influence their friends in their decision of which product to use. We propose two models for the spread of influence of competing technologies through a social network and consider the influence maximization problem from the follower’s perspective. In particular we assume the follower has a fixed budget available that can be used to target a subset of consumers and show that, although it is NP-hard to select the most influential subset to target, it is possible to give an efficient algorithm that is within 63 % of optimal. Our computational experiments show that by using knowledge of the social network and the set of consumers targeted by the competitor, the follower may in fact capture a majority of the market by targeting a relatively small set of the right consumers.

We introduce a novel frequent pattern mining approach to discover leaders and tribes in social networks. In particular, we consider social networks where users perform actions. Actions may be as simple as tagging resources (urls) as in del.icio.us, rating songs as in Yahoo! Music, or movies as in Yahoo! Movies, or users buying gadgets such as cameras, handhelds, etc. and blogging a review on the gadgets. The assumption is that actions performed by a user can be seen by their network friends. Users seeing their friends ’ actions are sometimes tempted to perform those actions. We are interested in the problem of studying the propagation of such “influence”, and on this basis, identifying which users are leaders when it comes to setting the trend for performing various actions. We consider alternative definitions of leaders based on frequent patterns and develop algorithms for their efficient discovery. Our definitions are based on observing the way influence propagates in a time window, as the window is moved in time. Given a social graph and a table of user actions, our algorithms can discover leaders of various flavors by making one pass over the actions table. We run detailed experiments to evaluate the utility and scalability of our algorithms on real-life data. The results of our experiments confirm on the one hand, the efficiency of the proposed algorithm, and on the other hand, the effectiveness and relevance of the overall framework. To the best of our knowledge, this the first frequent pattern based approach to social network mining.

Abstract. In this paper we consider the problem of learning hidden independent cascade social networks using exact value injection queries. These queries involve activating and suppressing agents in the target network. We develop an algorithm that optimally learns an arbitrary social network of size n using O(n 2) queries, matching the information theoretic lower bound we prove for this problem. We also consider the case when the target social network forms a tree and show that the learning problem takes Θ(n log(n)) queries. We also give an approximation algorithm for finding an influential set of nodes in the network, without resorting to learning its structure. Finally, we discuss some limitations of our approach, and limitations of path-based methods, when non-exact value injection queries are used. 1

Abstract. In this paper we examine the diffusion of competing rumors in social networks. Two players select a disjoint subset of nodes as initiators of the rumor propagation, seeking to maximize the number of persuaded nodes. We use concepts of game theory and location theory and model the selection of starting nodes for the rumors as a strategic game. We show that computing the optimal strategy for both the first and the second player is NP-complete, even in a most restricted model. Moreover we prove that determining an approximate solution for the first player is NP-complete as well. We analyze several heuristics and show that—counter-intuitively—being the first to decide is not always an advantage, namely there exist networks where the second player can convince more nodes than the first, regardless of the first player’s decision. 1

Abstract. We consider the spread maximization problem that was defined by Domingos and Richardson [7, 22]. In this problem, we are given a social network represented as a graph and are required to find the set of the most “influential ” individuals that by introducing them with a new technology, we maximize the expected number of individuals in the network, later in time, that adopt the new technology. This problem has applications in viral marketing, where a company may wish to spread the rumor of a new product via the most influential individuals in popular social networks such as Myspace and Blogsphere. The spread maximization problem was recently studied in several models of social networks [14, 15, 20]. In this short paper we study this problem in the context of the well studied probabilistic voter model. We provide very simple and efficient algorithms for solving this problem. An interesting special case of our result is that the most natural heuristic solution, which picks the nodes in the network with the highest degree, is indeed the optimal solution.