Ranking influential nodes in networks from partial information
Silvia Bartolucci, Fabio Caccioli, Francesco Caravelli, Pierpaolo Vivo
备注：
13 pages, 7 figures. Significant changes in title and content (references added, more data sets analyzed, effect of network sparsity studied in more detail)
Many complex systems exhibit a natural hierarchy in which elements can be ranked according to a notion of "influence". While the complete and accurate knowledge of the interactions between constituents is ordinarily required for the computation of nodes' influence, using a low-rank approximation we show that in a variety of contexts local information about the neighborhoods of nodes is enough to reliably estimate how influential they are, without the need to infer or reconstruct the whole map of interactions. Our framework is successful in approximating with high accuracy different incarnations of influence in systems as diverse as the WWW PageRank, trophic levels of ecosystems, upstreamness of industrial sectors in complex economies, and centrality measures of social networks, as long as the underlying network is not exceedingly sparse. We also discuss the implications of this "emerging locality" on the approximate calculation of non-linear network observables.
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…
The identification of influential nodes in complex network can be very challenging. If the network has a community structure, centrality measures may fail to identify the complete set of influential nodes, as the hubs and other central nodes of the network may lie inside only one community. Here we define a bipartite clustering coefficient that, by taking differently structured clusters into account, can find important nodes across communities.
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…
The network of networks(NON) research is focused on studying the properties of n interdependent networks which is ubiquitous in the real world. Identifying the influential nodes in the network of networks is theoretical and practical significance. However, it is hard to describe the structure property of the NON based on traditional methods. In this paper, a new method is proposed to identify the influential nodes in the network of networks base on the evidence theory. The proposed method can fuse different kinds of relationship between the network components to constructed a comprehensive sim…
The Identification of the influential nodes in networks is one of the most promising domains. In this paper, we present an improved iterative resource allocation (IIRA) method by considering the centrality information of neighbors and the influence of spreading rate for a target node. Comparing with the results of the Susceptible Infected Recovered (SIR) model for four real networks, the IIRA method could identify influential nodes more accurately than the tradition IRA method. Specially, in the Erdos network, the Kendall's tau could be enhanced 23\% when the spreading rate is 0.12. In the Pro…
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…
Identifying influential nodes that can jointly trigger the maximum influence spread in networks is a fundamental problem in many applications such as viral marketing, online advertising, and disease control. Most existing studies assume that social influence is static and they fail to capture the dynamics of influence in reality. In this work, we address the dynamic influence challenge by designing efficient streaming methods that can identify influential nodes from highly dynamic node interaction streams. We first propose a general time-decaying dynamic interaction network (TDN) model to mode…
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…
Identifying influential nodes in the complex networks is of theoretical and practical significance. There are many methods are proposed to identify the influential nodes in the complex networks. In this paper, a local structure entropy which is based on the degree centrality and the statistical mechanics is proposed to identifying the influential nodes in the complex network. In the definition of the local structure entropy, each node has a local network, the local structure entropy of each node is equal to the structure entropy of the local network. The main idea in the local structure entrop…
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…
In this paper, we tackle a challenging problem inherent in a series of applications: tracking the influential nodes in dynamic networks. Specifically, we model a dynamic network as a stream of edge weight updates. This general model embraces many practical scenarios as special cases, such as edge and node insertions, deletions as well as evolving weighted graphs. Under the popularly adopted linear threshold model and independent cascade model, we consider two essential versions of the problem: finding the nodes whose influences passing a user specified threshold and finding the top-$k$ most in…
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…
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…
Recently an increasing amount of research is devoted to the question of how the most influential nodes (seeds) can be found effectively in a complex network. There are a number of measures proposed for this purpose, for instance, high-degree centrality measure reflects the importance of the network topology and has a reasonable runtime performance to find a set of nodes with highest degree, but they do not have a satisfactory dissemination potentiality in the network due to having many common neighbors ($\mbox{CN}^{(1)}$) and common neighbors of neighbors ($\mbox{CN}^{(2)}$). This flaw holds i…
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…
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…
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…
In graph theory and network analysis, node degree is defined as a simple but powerful centrality to measure the local influence of node in a complex network. Preferential attachment based on node degree has been widely adopted for modeling network growth. However, many evidences exist which show deviation of real network growth from what a pure degree-based model suggests. It seems that node degree is not a reliable measure for predicting the preference of newcomers in attaching to the network, or at least, it does not tell the whole story. In this paper, we argue that there is another dimensi…
Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in case of epidemic spreading, during intentional attacks on complex networks. A lot of research is done to devise centrality measures which could efficiently identify the most influential nodes in the network. There are two major approaches to the problem: On one hand, deterministic strategies that exploit knowledge about the overall network topology in order …
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors measure relevant process variables at appropriate sampling rates, to provide time series as primary sources for system diagnostics. However, high-dimensionality, non-linearity and non-stationarity of data remain a major challenge to effectively diagnose rare or new system issues by merely using model-based approaches. To reduce the causal search space, we validate…
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…
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…
Influential Simplices Mining via Simplicial Convolutional Network
Institute of Fundamental and Frontier Studies, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院）；Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China（电子科技大学长三角研究院（湖州））；School of Cyber Science and Technology, University of Science and Technology of China（中国科学技术大学网络空间安全学院）
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…
Thermalization is one of the most important phenomena in statistical physics. Often, the transition probabilities between different states in the phase space is or can be approximated by constants. In this case, the system can be described by Markovian transition kernels, and when the phase space is discrete, by Markov chains. In this paper, we introduce a macroscopic entropy on the states of paths of length $k$ and, studying the recursion relation, obtain a fixed point entropy. This analysis leads to a centrality approach to Markov chains entropy.
In this paper I'll speak about non-spectral clustering techniques and see how a node ordering based on centrality measures can improve the quality of communities detected. I'll also discuss an improvement to existing techniques, which further improves modularity.
Katz centrality is a popular network centrality measure. It takes a (weighted) count of all walks starting at each node, with an additional damping factor of $α$ that tunes the influence of walks as lengths increase. We introduce a tool to compare different centrality measures in terms of their node rankings, which takes into account that a relative ranking of two nodes by a centrality measure is unreliable if their scores are within a margin of error of one another. We employ this tool to understand the effect of the $α$-parameter on the lengths of walks that significantly affect the ranking …
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…
Complex networks have gained more attention from the last few years. The size of real-world complex networks, such as online social networks, WWW network, collaboration networks, is increasing exponentially with time. It is not feasible to collect the complete data and store and process it. In the present work, we propose a method to estimate the degree centrality rank of a node without having the complete structure of the graph. The proposed algorithm uses the degree of a node and power-law exponent of the degree distribution to calculate the ranking. Simulation results on the Barabasi-Albert…
High-centrality nodes have disproportionate influence on the behavior of a network; therefore controlling such nodes can efficiently steer the system to a desired state. Existing multiplex centrality measures typically rank nodes assuming the layers are qualitatively similar. Many real systems, however, are comprised of networks heterogeneous in nature, for example, social networks may have both agnostic and affiliative layers. Here, we use rank aggregation methods to identify intervention targets in multiplex networks when the structure, the dynamics, and our intervention goals are qualitativ…
Identifying the most influential individuals can provide invaluable help in developing and deploying effective viral marketing strategies. Previous studies mainly focus on designing efficient algorithms or heuristics to find top-K influential nodes on a given static social network. While, as a matter of fact, real-world social networks keep evolving over time and a recalculation upon the changed network inevitably leads to a long running time, significantly affecting the efficiency. In this paper, we observe from real-world traces that the evolution of social network follows the preferential a…
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…
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 re…
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…
We formulate and propose an algorithm (MultiRank) for the ranking of nodes and layers in large multiplex networks. MultiRank takes into account the full multiplex network structure of the data and exploits the dual nature of the network in terms of nodes and layers. The proposed centrality of the layers (influences) and the centrality of the nodes are determined by a coupled set of equations. The basic idea consists in assigning more centrality to nodes that receive links from highly influential layers and from already central nodes. The layers are more influential if highly central nodes are …
Ranking node importance is crucial in understanding network structure and function on complex networks. Degree, h-index and coreness are widely used, but which one is more proper to a network associated with a dynamical process, e.g. SIR spreading process, is still unclear. To fill this gap, a, which is extracted from the fitting function (f(x)=1-1/(e^(2a(x-b))+1)) of the average number of nodes in each radius of the neighborhood of a node, is proposed. Experiment results which are carried out on twenty real-world networks show that a can classify which of the three measures (degree, h-index a…
Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the components of the system that compete for survival and success based on the outcomes of the competitions between them. Here we propose a ranking method based on the random walk on the network representing the competitors as nodes and competitions as directed edges with asymmetric weights. We use the edge weights and node degrees to define the gradient on each …
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…
For network scientists, it has always been an interesting problem to identify the influential nodes in a given network. The k-shell decomposition method is a widely used method which assigns a shell-index value to each node based on its influential power. The k-shell method requires the global information of the network to compute the shell-index of a node that is infeasible for large-scale real-world dynamic networks. In this work, we propose a method to estimate the shell-index of a node using its local information. We also propose hill-climbing based approach to hit the top-ranked nodes in …
To rank nodes in quasi-hierarchical networks of social nature, it is necessary to carry out a detailed analysis of the network and evaluate the results obtained according to all the given criteria and identify the most influential nodes. Existing ranking algorithms in the overwhelming majority estimate such networks in general, which does not allow to clearly determine the influence of nodes among themselves. In the course of the study, an analysis of the results of known algorithms for ranking the nodes of HITS, PageRank and compares the obtained data with the expert evaluation of the network…
Recent research on finding important intermediate nodes in a network suspected to contain criminal activity is highly dependent on network centrality values. Betweenness centrality, for example, is widely used to rank the nodes that act as brokers in the shortest paths connecting all source and all the end nodes in a network. However both the shortest path node betweenness and the linearly scaled betweenness can only show rankings for all the nodes in a network. In this paper we explore the mathematical concept of pair-dependency on intermediate nodes, adapting the concept to criminal relation…
Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a target node and the node set with the highest $k$-core value, we present an improved method to generate the ranking list to evaluate the node spreading influence. Comparing with the epidemic process results for four real networks and the Barabási-Albert network, the parameterless method could identify the node spreading influence more accurately than the ones…
The safety and robustness of the network have attracted the attention of people from all walks of life, and the damage of several key nodes will lead to extremely serious consequences. In this paper, we proposed the clustering H-index mixing (CHM) centrality based on the H- index of the node itself and the relative distance of its neighbors. Starting from the node itself and combining with the topology around the node, the importance of the node and its spreading capability were determined. In order to evaluate the performance of the proposed method, we use Susceptible-Infected-Recovered (SIR)…
