Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on social network is a global process, it is commonly believed that measuring the influence of nodes inevitably requires the knowledge of the entire network. Employing percolation theory, we show that the spreading process displays a nucleation behavior: once a piece of information spread from the seeds to more than a small characteristic number of nodes, it reaches a point of no return and will quickly reach the percolation cluster, regardless of the entire network structure, otherwise the spreading will be contained locally. Thus, we find that, without the knowledge of entire network, any nodes' global influence can be accurately measured using this characteristic number, which is independent of the network size. This motivates an efficient algorithm with constant time complexity on the long standing problem of best seed spreaders selection, with performance remarkably close to the true optimum.
Identifying influential spreaders is crucial for understanding and controlling spreading processes on social networks. Via assigning degree-dependent weights onto links associated with the ground node, we proposed a variant to a recent ranking algorithm named LeaderRank [L. Lv et al., PLoS ONE 6 (2011) e21202]. According to the simulations on the standard SIR model, the weighted LeaderRank performs better than LeaderRank in three aspects: (i) the ability to find out more influential spreaders, (ii) the higher tolerance to noisy data, and (iii) the higher robustness to intentional attacks.
How to identify the influential spreaders in social networks is crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases and rumors, and so on. In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks. The comparison between the gravity centrality index and some well-known centralities, such as degree centrality, betweenn…
Finding influential spreaders of information and disease in networks is an important theoretical problem, and one of considerable recent interest. It has been almost exclusively formulated as a node-ranking problem -- methods for identifying influential spreaders rank nodes according to how influential they are. In this work, we show that the ranking approach does not necessarily work: the set of most influential nodes depends on the number of nodes in the set. Therefore, the set of $n$ most important nodes to vaccinate does not need to have any node in common with the set of $n+1$ most import…
Identifying a set of influential spreaders in complex networks plays a crucial role in effective information spreading. A simple strategy is to choose top-$r$ ranked nodes as spreaders according to influence ranking method such as PageRank, ClusterRank and $k$-shell decomposition. Besides, some heuristic methods such as hill-climbing, SPIN, degree discount and independent set based are also proposed. However, these approaches suffer from a possibility that some spreaders are so close together that they overlap sphere of influence or time consuming. In this report, we present a simply yet effec…
Spreading is a ubiquitous process in the social, biological and technological systems. Therefore, identifying influential spreaders, which is important to prevent epidemic spreading and to establish effective vaccination strategies, is full of theoretical and practical significance. In this paper, a weighted h-index centrality based on virtual nodes extension is proposed to quantify the spreading influence of nodes in complex networks. Simulation results on real-world networks reveal that the proposed method provides more accurate and more consistent ranking than the five classical methods. Mo…
An efficient strategy for the identification of influential spreaders that could be used to control epidemics within populations would be of considerable importance. Generally, populations are characterized by its community structures and by the heterogeneous distributions of weak ties among nodes bridging over communities. A strategy for community networks capable of identifying influential spreaders that accelerate the spread of disease is here proposed. In this strategy, influential spreaders serve as target nodes. This is based on the idea that, in k-shell decomposition, weak ties and stro…
Identifying the most influential spreaders is one of outstanding problems in physics of complex systems. So far, many approaches have attempted to rank the influence of nodes but there is still the lack of accuracy to single out influential spreaders. Here, we directly tackle the problem of finding important spreaders by solving analytically the expected size of epidemic outbreaks when spreading originates from a single seed. We derive and validate a theory for calculating the size of epidemic outbreaks with a single seed using a message-passing approach. In addition, we find that the probabil…
Most centralities proposed for identifying influential spreaders on social networks to either spread a message or to stop an epidemic require the full topological information of the network on which spreading occurs. In practice, however, collecting all connections between agents in social networks can be hardly achieved. As a result, such metrics could be difficult to apply to real social networks. Consequently, a new approach for identifying influential people without the explicit network information is demanded in order to provide an efficient immunization or spreading strategy, in a practi…
Identifying influential spreaders in complex networks is a crucial problem which relates to wide applications. Many methods based on the global information such as $k$-shell and PageRank have been applied to rank spreaders. However, most of related previous works overwhelmingly focus on the number of paths for propagation, while whether the paths are diverse enough is usually overlooked. Generally, the spreading ability of a node might not be strong if its propagation depends on one or two paths while the other paths are dead ends. In this Letter, we introduced the concept of path diversity an…
Recent research [1] has suggested that coreness, and not degree, constitutes a better topological descriptor to identifying influential spreaders in complex networks. This hypothesis has been verified in the context of disease spreading. Here, we instead focus on rumor spreading models, which are more suited for social contagion and information propagation. To this end, we perform extensive computer simulations on top of several real-world networks and find opposite results. Namely, we show that the spreading capabilities of the nodes do not depend on their $k$-core index, which instead determ…
Among the consequences of the disordered interaction topology underlying many social, techno- logical and biological systems, a particularly important one is that some nodes, just because of their position in the network, may have a disproportionate effect on dynamical processes mediated by the complex interaction pattern. For example, the early adoption by an opinion leader in a social network may change the fate of a commercial product, or just a few super-spreaders may determine the virality of a meme in social media. Despite many recent efforts, the formulation of an accurate method to opt…
Identifying the most influential spreaders is an important issue in controlling the spreading processes in complex networks. Centrality measures are used to rank node influence in a spreading dynamics. Here we propose a node influence measure based on the centrality of a node and its neighbors' centrality, which we call the neighborhood centrality. By simulating the spreading processes in six real-world networks, we find that the neighborhood centrality greatly outperforms the basic centrality of a node such as the degree and coreness in ranking node influence and identifying the most influent…
Identifying the most influential spreaders is an important issue in understanding and controlling spreading processes on complex networks. Recent studies showed that nodes located in the core of a network as identified by the k-shell decomposition are the most influential spreaders. However, through a great deal of numerical simulations, we observe that not in all real networks do nodes in high shells are very influential: in some networks the core nodes are the most influential which we call true core, while in others nodes in high shells, even the innermost core, are not good spreaders which…
This study proposes the usage of a method called VoteRank, created by Zhang et al. (2016), to identify influential nodes on patent citation networks. In addition, it proposes enhanced VoteRank algorithms, extending the Zhang et al. work. These novel algorithms comprise a reduction on the voting ability of the nodes affected by a chosen spreader if the nodes are distant from the spreader. One method uses a reduction factor that is linear regarding the distance from the spreader, which we called VoteRank-LRed. The other method uses a reduction factor that is exponential concerning the distance f…
The identification of the most influential spreaders in networks is important to control and understand the spreading capabilities of the system as well as to ensure an efficient information diffusion such as in rumor-like dynamics. Recent works have suggested that the identification of influential spreaders is not independent of the dynamics being studied. For instance, the key disease spreaders might not necessarily be so when it comes to analyze social contagion or rumor propagation. Additionally, it has been shown that different metrics (degree, coreness, etc) might identify different infl…
The burst in the use of online social networks over the last decade has provided evidence that current rumor spreading models miss some fundamental ingredients in order to reproduce how information is disseminated. In particular, recent literature has revealed that these models fail to reproduce the fact that some nodes in a network have an influential role when it comes to spread a piece of information. In this work, we introduce two mechanisms with the aim of filling the gap between theoretical and experimental results. The first model introduces the assumption that spreaders are not always …
Influence maximization is the problem of finding the set of nodes of a network that maximizes the size of the outbreak of a spreading process occurring on the network. Solutions to this problem are important for strategic decisions in marketing and political campaigns. The typical setting consists in the identification of small sets of initial spreaders in very large networks. This setting makes the optimization problem computationally infeasible for standard greedy optimization algorithms that account simultaneously for information about network topology and spreading dynamics, leaving space …
Networks portray a multitude of interactions through which people meet, ideas are spread, and infectious diseases propagate within a society. Identifying the most efficient "spreaders" in a network is an important step to optimize the use of available resources and ensure the more efficient spread of information. Here we show that, in contrast to common belief, the most influential spreaders in a social network do not correspond to the best connected people or to the most central people (high betweenness centrality). Instead, we find: (i) The most efficient spreaders are those located within t…
Identifying influential nodes in complex networks has received increasing attention for its great theoretical and practical applications in many fields. Traditional methods, such as degree centrality, betweenness centrality, closeness centrality, and coreness centrality, have more or less disadvantages in detecting influential nodes, which have been illustrated in related literatures. Recently, the h-index, which is utilized to measure both the productivity and citation impact of the publications of a scientist or scholar, has been introduced to the network world to evaluate a node's spreading…
We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should be considered explicitly. An edge connecting nodes i and j may differ in its importance for spreading from i to j and from j to i. The key issue is whether node j, after infected by i through the edge, would reach out to other nodes that i itself could not reach directly. It becomes necessary to invoke two unequal weights wij and wji characterizing the import…
Identifying the most influential spreaders is important to understand and control the spreading process in a network. As many real-world complex systems can be modeled as multilayer networks, the question of identifying important nodes in multilayer network has attracted much attention. Existing studies focus on the multilayer network structure, while neglecting how the structural and dynamical coupling of multiple layers influence the dynamical importance of nodes in the network. Here we investigate on this question in an information-disease coupled spreading dynamics on multiplex networks. F…
The identification of which nodes are optimal seeds for spreading processes on a network is a non-trivial problem that has attracted much interest recently. While activity has mostly focused on non-recurrent type of dynamics, here we consider the problem for the Susceptible-Infected-Susceptible (SIS) spreading model, where an outbreak seeded in one node can originate an infinite activity avalanche. We apply the theoretical framework for avalanches on networks proposed by Larremore et al. [Phys. Rev. E 85, 066131 (2012)], to obtain detailed quantitative predictions for the spreading influence o…
We introduce a new method to efficiently approximate the number of infections resulting from a given initially-infected node in a network of susceptible individuals. Our approach is based on counting the number of possible infection walks of various lengths to each other node in the network. We analytically study the properties of our method, in particular demonstrating different forms for SIS and SIR disease spreading (e.g. under the SIR model our method counts self-avoiding walks). In comparison to existing methods to infer the spreading efficiency of different nodes in the network (based on…
It is widely acknowledged that the initial spreaders play an important role for the wide spreading of information in complex networks. Thus, a variety of centrality-based methods have been proposed to identify the most influential spreaders. However, most of the existing studies have overlooked the fact that in real social networks it is more costly and difficult to convince influential individuals to act as initial spreaders, resulting in a high risk in maximizing the spreading. In this paper, we address this problem on the basis of the assumption that large-degree nodes are activated with a …
Social networks constitute a new platform for information propagation, but its success is crucially dependent on the choice of spreaders who initiate the spreading of information. In this paper, we remove edges in a network at random and the network segments into isolated clusters. The most important nodes in each cluster then form a group of influential spreaders, such that news propagating from them would lead to an extensive coverage and minimal redundancy. The method well utilizes the similarities between the pre-percolated state and the coverage of information propagation in each social c…
The reversible spreading processes with repeated infection widely exist in nature and human society, such as gonorrhea propagation and meme spreading. Identifying influential spreaders is an important issue in the reversible spreading dynamics on complex networks, which has been given much attention. Except for structural centrality, the nodes' dynamical states play a significant role in their spreading influence in the reversible spreading processes. By integrating the number of outgoing edges and infection risks of node's neighbors into structural centrality, a new measure for identifying in…
With great theoretical and practical significance, locating influential nodes of complex networks is a promising issues. In this paper, we propose a dynamics-sensitive (DS) centrality that integrates topological features and dynamical properties. The DS centrality can be directly applied in locating influential spreaders. According to the empirical results on four real networks for both susceptible-infected-recovered (SIR) and susceptible-infected (SI) spreading models, the DS centrality is much more accurate than degree, $k$-shell index and eigenvector centrality.
Finding influential spreaders is a crucial task in the field of network analysis because of numerous theoretical and practical importance. These nodes play vital roles in the information diffusion process, like viral marketing. Many real-life networks are weighted networks, but relatively less work has been done for finding influential nodes in the case of weighted networks as compared to unweighted networks. In this paper, we propose a k-shell-based HookeRank (KSHR) algorithm to identify spreaders in weighted networks. First, we propose weighted k-shell centrality of the node u by using the k…
Searching for influential spreaders in complex networks is an issue of great significance for applications across various domains, ranging from the epidemic control, innovation diffusion, viral marketing, social movement to idea propagation. In this paper, we first display some of the most important theoretical models that describe spreading processes, and then discuss the problem of locating both the individual and multiple influential spreaders respectively. Recent approaches in these two topics are presented. For the identification of privileged single spreaders, we summarize several widely…
How to identify influential nodes in social networks is of theoretical significance, which relates to how to prevent epidemic spreading or cascading failure, how to accelerate information diffusion, and so on. In this Letter, we make an attempt to find \emph{effective multiple spreaders} in complex networks by generalizing the idea of the coloring problem in graph theory to complex networks. In our method, each node in a network is colored by one kind of color and nodes with the same color are sorted into an independent set. Then, for a given centrality index, the nodes with the highest centra…
Identifying the most influential spreaders that maximize information flow is a central question in network theory. Recently, a scalable method called "Collective Influence (CI)" has been put forward through collective influence maximization. In contrast to heuristic methods evaluating nodes' significance separately, CI method inspects the collective influence of multiple spreaders. Despite that CI applies to the influence maximization problem in percolation model, it is still important to examine its efficacy in realistic information spreading. Here, we examine real-world information flow in v…
Ranking the nodes' ability for spreading in networks is a fundamental problem which relates to many real applications such as information and disease control. In the previous literatures, a network decomposition procedure called k-shell method has been shown to effectively identify the most influential spreaders. In this paper, we find that the k-shell method have some limitations when it is used to rank all the nodes in the network. We also find that these limitations are due to considering only the links between the remaining nodes (residual degree) while entirely ignoring all the links conn…
A number of predictors have been suggested to detect the most influential spreaders of information in online social media across various domains such as Twitter or Facebook. In particular, degree, PageRank, k-core and other centralities have been adopted to rank the spreading capability of users in information dissemination media. So far, validation of the proposed predictors has been done by simulating the spreading dynamics rather than following real information flow in social networks. Consequently, only model-dependent contradictory results have been achieved so far for the best predictor.…
In social networks, the collective behavior of large populations can be shaped by a small set of influencers through a cascading process induced by "peer pressure". For large-scale networks, efficient identification of multiple influential spreaders with a linear algorithm in threshold models that exhibit a first-order transition still remains a challenging task. Here we address this issue by exploring the collective influence in general threshold models of behavior cascading. Our analysis reveals that the importance of spreaders is fixed by the subcritical paths along which cascades propagate…
We consider the problem of identifying the most influential nodes for a spreading process on a network when prior knowledge about structure and dynamics of the system is incomplete or erroneous. Specifically, we perform a numerical analysis where the set of top spreaders is determined on the basis of prior information that is artificially altered by a certain level of noise. We then measure the optimality of the chosen set by measuring its spreading impact in the true system. Whereas we find that the identification of top spreaders is optimal when prior knowledge is complete and free of mistak…
In a diversified context with multiple social networking sites, heterogeneous activity patterns and different user-user relations, the concept of "information cascade" is all but univocal. Despite the fact that such information cascades can be defined in different ways, it is important to check whether some of the observed patterns are common to diverse contagion processes that take place on modern social media. Here, we explore one type of information cascades, namely, those that are time-constrained, related to two kinds of socially-rooted topics on Twitter. Specifically, we show that in bot…
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…
Modelling information cascades over online social networks is important in fields from marketing to civil unrest prediction, however the underlying network structure strongly affects the probability and nature of such cascades. Even with simple cascade dynamics the probability of large cascades are almost entirely dictated by network properties, with well-known networks such as Erdos-Renyi and Barabasi-Albert producing wildly different cascades from the same model. Indeed, the notion of 'superspreaders' has arisen to describe highly influential nodes promoting global cascades in a social netwo…
Identifying influential nodes in networks is a significant and challenging task. Among many centrality indices, the $k$-shell index performs very well in finding out influential spreaders. However, the traditional method for calculating the $k$-shell indices of nodes needs the global topological information, which limits its applications in large-scale dynamically growing networks. Recently, L\@ü \emph{et al.} [Nature Communications 7 (2016) 10168] proposed a novel asynchronous algorithm to calculate the $k$-shell indices, which is suitable to deal with large-scale growing networks. In this pa…
As an important type of dynamics on complex networks, spreading is widely used to model many real processes such as the epidemic contagion and information propagation. One of the most significant research questions in spreading is to rank the spreading ability of nodes in the network. To this end, substantial effort has been made and a variety of effective methods have been proposed. These methods usually define the spreading ability of a node as the number of finally infected nodes given that the spreading is initialized from the node. However, in many real cases such as advertising and medic…
Influence Maximization (IM) aims at finding the most influential users in a social network, i. e., users who maximize the spread of an opinion within a certain propagation model. Previous work investigated the correlation between influence spread and nodal centrality measures to bypass more expensive IM simulations. The results were promising but incomplete, since these studies investigated the performance (i. e., the ability to identify influential users) of centrality measures only in restricted settings, e. g., in undirected/unweighted networks and/or within a propagation model less common …
The generalized $H(n)$ Hirsch index of order $n$ has been recently introduced and shown to interpolate between the degree and the $K$-core centrality in networks. We provide a detailed analytical characterization of the properties of sets of nodes having the same $H(n)$, within the annealed network approximation. The connection between the Hirsch indices and the degree is highlighted. Numerical tests in synthetic uncorrelated networks and real-world correlated ones validate the findings. We also test the use of the Hirsch index for the identification of influential spreaders in networks, findi…
Rumor models consider that information transmission occurs with the same probability between each pair of nodes. However, this assumption is not observed in social networks, which contain influential spreaders. To overcome this limitation, we assume that central individuals have a higher capacity of convincing their neighbors than peripheral subjects. By extensive numerical simulations we find that the spreading is improved in scale-free networks when the transmission probability is proportional to PageRank, degree, and betweenness centrality. In addition, the results suggest that the spreadin…
The effective use of limited resources for controlling spreading processes on networks is of prime significance in diverse contexts, ranging from the identification of "influential spreaders" for maximizing information dissemination and targeted interventions in regulatory networks, to the development of mitigation policies for infectious diseases and financial contagion in economic systems. Solutions for these optimization tasks that are based purely on topological arguments are not fully satisfactory; in realistic settings the problem is often characterized by heterogeneous interactions and …
We consider the optimization problem of seeding a spreading process on a temporal network so that the expected size of the resulting outbreak is maximized. We frame the problem for a spreading process following the rules of the susceptible-infected-recovered model with temporal scale equal to the one characterizing the evolution of the network topology. We perform a systematic analysis based on a corpus of 12 real-world temporal networks and quantify the performance of solutions to the influence maximization problem obtained using different level of information about network topology and dynam…
Epidemics occur in all shapes and forms: infections propagating in our sparse sexual networks, rumours and diseases spreading through our much denser social interactions, or viruses circulating on the Internet. With the advent of large databases and efficient analysis algorithms, these processes can be better predicted and controlled. In this study, we use different characteristics of network organization to identify the influential spreaders in 17 empirical networks of diverse nature using 2 epidemic models. We find that a judicious choice of local measures, based either on the network's conn…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network science, which allow us to better conduct successful social advertisements, immunize a network against epidemics, discover drug target candidates and essential proteins, and prevent cascading breakdowns in power grids, financial markets and ecological systems. Inspired by the nested nature of real networks, we propose a decomposition method where at each step…
Social networks play a key role in studying various individual and social behaviors. To use social networks in a study, their structural properties must be measured. For offline social networks, the conventional procedure is surveying/interviewing a set of randomly-selected respondents. In many practical applications, inferring the network structure via sampling is too prohibitively costly. There are also applications in which it simply fails. For example, for optimal vaccination or employing influential spreaders for public health interventions, we need to efficiently and quickly target well-…
Centrality measures such as the degree, k-shell, or eigenvalue centrality can identify a network's most influential nodes, but are rarely usefully accurate in quantifying the spreading power of the vast majority of nodes which are not highly influential. The spreading power of all network nodes is better explained by considering, from a continuous-time epidemiological perspective, the distribution of the force of infection each node generates. The resulting metric, the \textit{expected force}, accurately quantifies node spreading power under all primary epidemiological models across a wide ran…
When analyzing the statistical and topological characteristics of complex networks, an effective and convenient way is to compute the centralities for recognizing influential and significant nodes or structures, yet most of them are restricted to local environment or some specific configurations. In this paper we propose a new centrality for nodes based on the von Neumann entropy, which allows us to investigate the importance of nodes in the view of spectrum eigenvalues distribution. By presenting the performances of this centrality with network examples in reality, it is shown that the von Ne…
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous studies pointed out that real-world multiplex networks display significant inter-layer correlations -- degree-degree correlation, edge overlap, node similarities -- able to make them robust against random and targeted failures of their individual components. Here, we show that inter-layer correlations are important also in the characterization of their $\mathbf{…
Human social behavior plays a crucial role in how pathogens like SARS-CoV-2 or fake news spread in a population. Social interactions determine the contact network among individuals, while spreading, requiring individual-to-individual transmission, takes place on top of the network. Studying the topological aspects of a contact network, therefore, not only has the potential of leading to valuable insights into how the behavior of individuals impacts spreading phenomena, but it may also open up possibilities for devising effective behavioral interventions. Because of the temporal nature of inter…
Viral marketing campaigns seek to recruit the most influential individuals to cover the largest target audience. This can be modeled as the well-studied maximum coverage problem. There is a related problem when the recruited nodes are connected. It is called the maximum connected cover problem. This problem ensures a strong coordination between the influential nodes which are the backbone of the marketing campaign. In this work, we are interested on both of these problems. Most of the related literature assumes knowledge about the topology of the network. Even in that case, the problem is know…
