Influential nodes in complex networks are typically defined as those nodes that maximize the asymptotic reach of a spreading process of interest. However, for practical applications such as viral marketing and online information spreading, one is often interested in maximizing the reach of the process in a short amount of time. The traditional definition of influencers in network-related studies from diverse research fields narrows down the focus to the late-time state of the spreading processes, leaving the following question unsolved: which nodes are able to initiate large-scale spreading processes, in a limited amount of time? Here, we find that there is a fundamental difference between the nodes -- which we call "fast influencers" -- that initiate the largest-reach processes in a short amount of time, and the traditional, "late-time" influencers. Stimulated by this observation, we provide an extensive benchmarking of centrality metrics with respect to their ability to identify both the fast and late-time influencers. We find that local network properties can be used to uncover the fast influencers. In particular, a parsimonious, local centrality metric (which we call social capital) achieves optimal or nearly-optimal performance in the fast influencer identification for all the analyzed empirical networks. Local metrics tend to be also competitive in the traditional, late-time influencer identification task.
In social and biological systems, the structural heterogeneity of interaction networks gives rise to the emergence of a small set of influential nodes, or influencers, in a series of dynamical processes. Although much smaller than the entire network, these influencers were observed to be able to shape the collective dynamics of large populations in different contexts. As such, the successful identification of influencers should have profound implications in various real-world spreading dynamics such as viral marketing, epidemic outbreaks and cascading failure. In this chapter, we first summari…
The integrity and functionality of many real-world complex systems hinge on a small set of pivotal nodes, or influencers. In different contexts, these influencers are defined as either structurally important nodes that maintain the connectivity of networks, or dynamically crucial units that can disproportionately impact certain dynamical processes. In practice, identification of the optimal set of influencers in a given system has profound implications in a variety of disciplines. In this review, we survey recent advances in the study of influencer identification developed from different persp…
A pivotal idea in network science, marketing research and innovation diffusion theories is that a small group of nodes -- called influencers -- have the largest impact on social contagion and epidemic processes in networks. Despite the long-standing interest in the influencers identification problem in socio-economic and biological networks, there is not yet agreement on which is the best identification strategy. State-of-the-art strategies are typically based either on heuristic centrality metrics or on analytic arguments that only hold for specific network topologies or peculiar dynamical re…
The identification of influential spreaders in complex networks is a popular topic in studies of network characteristics. Many centrality measures have been proposed to address this problem, but most have limitations. In this paper, a method for identifying influencers in complex networks via the local information dimensionality. The proposed method considers the local structural properties around the central node; therefore, the scale of locality only increases to half of the maximum value of the shortest distance from the central node. Thus, the proposed method considers the quasilocal infor…
The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network [1]; or, if immunized, would prevent the diffusion of a large scale epidemic [2,3]. Localizing this optimal, i.e. minimal, set of structural nodes, called influencers, is one of the most important problems in network science [4,5]. Despite the vast use of heuristic strategies to identify influential spreaders [6-14], the problem remains unsolved. Here, we map the problem onto optim…
Influence maximization is the problem of finding influential users, or nodes, in a graph so as to maximize the spread of information. It has many applications in advertising and marketing on social networks. In this paper, we study a highly generic version of influence maximization, one of optimizing influence campaigns by sequentially selecting "spread seeds" from a set of influencers, a small subset of the node population, under the hypothesis that, in a given campaign, previously activated nodes remain "persistently" active throughout and thus do not yield further rewards. This problem is i…
We elaborate on a linear time implementation of the Collective Influence (CI) algorithm introduced by Morone, Makse, Nature 524, 65 (2015) to find the minimal set of influencers in a network via optimal percolation. We show that the computational complexity of CI is O(N log N) when removing nodes one-by-one, with N the number of nodes. This is made possible by using an appropriate data structure to process the CI values, and by the finite radius l of the CI sphere. Furthermore, we introduce a simple extension of CI when l is infinite, the CI propagation (CI_P) algorithm, that considers the glo…
Influencer marketing has become a thriving industry with a global market value expected to reach 15 billion dollars by 2022. The advertising problem that such agencies face is the following: given a monetary budget find a set of appropriate influencers that can create and publish posts of various types (e.g. text, image, video) for the promotion of a target product. The campaign's objective is to maximize across one or multiple online social platforms some impact metric of interest, e.g. number of impressions, sales (ROI), or audience reach. In this work, we present an original continuous form…
We propose a generalized framework for influence maximization in large-scale, time evolving networks. Many real-life influence graphs such as social networks, telephone networks, and IP traffic data exhibit dynamic characteristics, e.g., the underlying structure and communication patterns evolve with time. Correspondingly, we develop a dynamic framework for the influence maximization problem, where we perform effective local updates to quickly adjust the top-k influencers, as the structure and communication patterns in the network change. We design a novel N-Family approach (N=1, 2, 3, ...) ba…
The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide crucial insights into social influence and behavior-adoption cascades on networks. In this paper, we introduce a model of a multi-stage complex contagion on networks. Agents at different stages --- which could, for example, represent differing levels of support for a social movement or differing levels of commitment to a certain product or idea --- exert different amounts of inf…
Adobe Research（Adobe研究院）；INRIA Lille - Nord Europe（法国里尔-北欧信息与自动化研究所）；University of British Columbia（不列颠哥伦比亚大学）
We study the online influence maximization problem in social networks under the independent cascade model. Specifically, we aim to learn the set of "best influencers" in a social network online while repeatedly interacting with it. We address the challenges of (i) combinatorial action space, since the number of feasible influencer sets grows exponentially with the maximum number of influencers, and (ii) limited feedback, since only the influenced portion of the network is observed. Under a stochastic semi-bandit feedback, we propose and analyze IMLinUCB, a computationally efficient UCB-based a…
In many complex networked systems, such as online social networks, activity originates at certain nodes and subsequently spreads on the network through influence. In this work, we consider the problem of modeling the spread of influence and the identification of influential entities in a complex network when nodal activation can happen via two different mechanisms. The first mechanism of activation stems from factors that are intrinsic to the node. The second mechanism comes from the influence of connected neighbors. After introducing the model, we provide an algorithm to mine for the influent…
Recently, the sizes of networks are always very huge, and they take on distributed nature. Aiming at this kind of network clustering problem, in the sight of local view, this paper proposes a fast network clustering algorithm in which each node is regarded as an agent, and each agent tries to maximize its local function in order to optimize network modularity defined by function Q, rather than optimize function Q from the global view as traditional methods. Both the efficiency and effectiveness of this algorithm are tested against computer-generated and real-world networks. Experimental result…
In this paper, we introduce a new algorithm allowing for generation of networks with heterogeneity of both node degrees and community sizes. The quality and efficiency of the algorithm is analyzed and compared to the other, so far the most popular algorithm which was proposed by Lancichinetti et al. We discuss the advantages and shortcomings of both algorithms indicating the areas of their potential application.
Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions than the ones obtained by the direct application of the algorithm. However, the procedure requires the calculation of the consensus matrix, which can be quite dense if (some of) the clusters of the input partitions are large. Consequently, the complexity can get dangerously close to quadratic, which makes the technique inapplicable on large graphs. Here we pres…
Michigan State University（密歇根州立大学）；University of South Florida（南佛罗里达大学）
The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this article, we use the PageRank function along with persistent homology to obtain a scalable graph descriptor and utilize it to compare the similarities between graphs. For a given graph $G(V,E)$, our descriptor can be computed in $O(|E|α(|V|))$, where $α$ is the inverse Ackermann function which makes it scalable and computable on massive graphs. We show the effectiveness of our method by utilizing it on multiple shape mesh datasets.
