Ekaterina Dudkina, Michelangelo Bin, Jane Breen, Emanuele Crisostomi, Pietro Ferraro, Steve Kirkland, Jakub Marecek, Roderick Murray-Smith, Thomas Parisini, Lew… 展开作者
Ekaterina Dudkina, Michelangelo Bin, Jane Breen, Emanuele Crisostomi, Pietro Ferraro, Steve Kirkland, Jakub Marecek, Roderick Murray-Smith, Thomas Parisini, Lewi Stone, Serife Yilmaz, Robert Shorten
The ranking of nodes in a network according to their ``importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The current COVID-19 pandemic has recently rejuvenated the interest in this problem, as it is related to the selection of which individuals should be tested in a population of asymptomatic individuals, or which individuals should be vaccinated first. Motivated by the COVID-19 spreading dynamics, in this paper we review the most popular methods for node ranking in undirected unweighted graphs, and compare their performance in a benchmark realistic network, that takes into account the community-based structure of society. Also, we generalize a classic benchmark network originally proposed by Newman for ranking nodes in unweighted graphs, to show how ranks change in the weighted case.
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.
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…
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…
Random teleportation is a necessary evil for ranking and clustering directed networks based on random walks. Teleportation enables ergodic solutions, but the solutions must necessarily depend on the exact implementation and parametrization of the teleportation. For example, in the commonly used PageRank algorithm, the teleportation rate must trade off a heavily biased solution with a uniform solution. Here we show that teleportation to links rather than nodes enables a much smoother trade-off and effectively more robust results. We also show that, by not recording the teleportation steps of th…
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)…
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…
Closeness centrality is one way of measuring how central a node is in the given network. The closeness centrality measure assigns a centrality value to each node based on its accessibility to the whole network. In real life applications, we are mainly interested in ranking nodes based on their centrality values. The classical method to compute the rank of a node first computes the closeness centrality of all nodes and then compares them to get its rank. Its time complexity is $O(n \cdot m + n)$, where $n$ represents total number of nodes, and $m$ represents total number of edges in the network…
Recent advances in graph theory suggest that is possible to identify the oldest nodes of a network using only the graph topology. Here we report on applications to heterogeneous real world networks. To this end, and in order to gain new insights, we propose the theoretical framework of the Estrada communicability. We apply it to two technological networks (an underground, the diffusion of a software worm in a LAN) and to a third network representing a cholera outbreak. In spite of errors introduced in the adjacency matrix of their graphs, the identification of the oldest nodes is feasible, wit…
Identifying the importance of nodes of complex networks is of interest to the research of Social Networks, Biological Networks etc.. Current researchers have proposed several measures or algorithms, such as betweenness, PageRank and HITS etc., to identify the node importance. However, these measures are based on different aspects of properties of nodes, and often conflict with the others. A reasonable, fair standard is needed for evaluating and comparing these algorithms. This paper develops a framework as the standard for ranking the importance of nodes. Four intuitive rules are suggested to …
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…
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…
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 …
PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of science, the relation between the algorithm's efficacy and properties of the network on which it acts has not yet been fully understood. We study here PageRank's performance on a network model supported by real data, and show that realistic temporal effects make PageRank fail in individuating the most valuable nodes for a broad range of model parameters. Results o…
Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchi…
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 …
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…
Link directions are essential to the functionality of networks and their prediction is helpful towards a better knowledge of directed networks from incomplete real-world data. We study the problem of predicting the directions of some links by using the existence and directions of the rest of links. We propose a solution by first ranking nodes in a specific order and then predicting each link as stemming from a lower-ranked node towards a higher-ranked one. The proposed ranking method works recursively by utilizing local indicators on multiple scales, each corresponding to a subgraph extracted …
Many systems, ranging from biological and engineering systems to social systems, can be modeled as directed networks, with links representing directed interaction between two nodes. To assess the importance of a node in a directed network, various centrality measures based on different criteria have been proposed. However, calculating the centrality of a node is often difficult because of the overwhelming size of the network or the incomplete information about the network. Thus, developing an approximation method for estimating centrality measures is needed. In this study, we focus on modular …
Information is a valuable asset for agents in socio-economic systems, a significant part of the information being entailed into the very network of connections between agents. The different interlinkages patterns that agents establish may, in fact, lead to asymmetries in the knowledge of the network structure; since this entails a different ability of quantifying relevant systemic properties (e.g. the risk of financial contagion in a network of liabilities), agents capable of providing a better estimate of (otherwise) unaccessible network properties, ultimately have a competitive advantage. In…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only their ranking by prestige. We propose a criterion of network growth that explicitly relies on the ranking of the nodes according to any prestige measure, be it topological or not. The resulting network has a scale-free degree distribution when the probability to link a target node is any power law function of its rank, even when one has only partial informatio…
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.
Given a real-world graph, how can we measure relevance scores for ranking and link prediction? Random walk with restart (RWR) provides an excellent measure for this and has been applied to various applications such as friend recommendation, community detection, anomaly detection, etc. However, RWR suffers from two problems: 1) using the same restart probability for all the nodes limits the expressiveness of random walk, and 2) the restart probability needs to be manually chosen for each application without theoretical justification. We have two main contributions in this paper. First, we propo…
This paper studies the problem of identifying the contagion source when partial timestamps of a contagion process are available. We formulate the source localization problem as a ranking problem on graphs, where infected nodes are ranked according to their likelihood of being the source. Two ranking algorithms, cost-based ranking (CR) and tree-based ranking (TR), are proposed in this paper. Experimental evaluations with synthetic and real-world data show that our algorithms significantly improve the ranking accuracy compared with four existing algorithms.
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…
A key task in social network and other complex network analysis is role analysis: describing and categorizing nodes according to how they interact with other nodes. Two nodes have the same role if they interact with equivalent sets of neighbors. The most fundamental role equivalence is automorphic equivalence. Unfortunately, the fastest algorithms known for graph automorphism are nonpolynomial. Moreover, since exact equivalence may be rare, a more meaningful task is to measure the role similarity between any two nodes. This task is closely related to the structural or link-based similarity pro…
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…
Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social networks where people are involved in different types of relationships and interact through various forms of communication media. The ranking of nodes in multiplex networks is one of the most pressing and challenging tasks that research on complex networks is currently facing. When pairs of nodes can be connected through multiple links and in multiple layer…
Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative model based on an interplay between community and hierarchical structures. It assumes that each node has a preference in the interaction mechanism and nodes with the same preference are more likely to interact, while heterogeneous interactions are still allowed. The sparsity of the network is exploited for implementing a more efficient algorithm. We demonstra…
In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as "superspreaders", are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resourc…
When we search online for content, we are constantly exposed to rankings. For example, web search results are presented as a ranking, and online bookstores often show us lists of best-selling books. While popularity-based ranking algorithms (like Google's PageRank) have been extensively studied in previous works, we still lack a clear understanding of their potential systemic consequences. In this work, we fill this gap by introducing a new model of network growth that allows us to compare the properties of the networks generated under the influence of different ranking algorithms. We show tha…
Faculty of Information Studies in Novo Mesto（新梅斯托信息研究学院）；Universitat Pompeu Fabra（庞培法布拉大学）；Jožef Stefan Institute（约瑟夫·斯特凡研究所）；University of Ljubljana（卢布尔雅那大学）
Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as features, and use two indepen…
In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a \textit{long-range interaction} between them, does not exhibit concentration phenomena typical of spectral rankings which take into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems.
Columbia University（哥伦比亚大学）；Santa Fe Institute（圣塔菲研究所）；University of Colorado（科罗拉多大学）
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that interactions are more likely to occur between individuals with similar ranks. It provides a natural statistical significance test for the inferred hierarchy, and it can be used to perform inference tasks such as predicting the existence or direction of edges. The ranking is obtained by solving a linear system of equations, which is sparse if the network is; th…
Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep understanding of how existing ranking algorithms perform, and which are their possible biases that may impair their effectivene…
Methods for ranking the importance of nodes in a network have a rich history in machine learning and across domains that analyze structured data. Recent work has evaluated these methods though the seed set expansion problem: given a subset $S$ of nodes from a community of interest in an underlying graph, can we reliably identify the rest of the community? We start from the observation that the most widely used techniques for this problem, personalized PageRank and heat kernel methods, operate in the space of landing probabilities of a random walk rooted at the seed set, ranking nodes according…
Ranking algorithms are pervasive in our increasingly digitized societies, with important real-world applications including recommender systems, search engines, and influencer marketing practices. From a network science perspective, network-based ranking algorithms solve fundamental problems related to the identification of vital nodes for the stability and dynamics of a complex system. Despite the ubiquitous and successful applications of these algorithms, we argue that our understanding of their performance and their applications to real-world problems face three fundamental challenges: (i) R…
In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from practical points of view. In this contribution we present a module-based method to efficiently break complex networks. The procedure first identifies the communities in which the network can be represented, then it deletes the nodes (edges) that connect different modules by its order in the betweenness centrality ranking list. We illustrate the method by applying it to various well known examples of social, infrastructure, and biological netw…
In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most real situations, only limited sub-structures of entire networks are available, and therefore the reliability of the order relationships in sampled networks requires investigation. With a set of randomly sampled nodes from the underlying original networks, we rank individual nodes by three centrality measures: degree, betweenness, and closeness. The higher-ran…
A model for efficient dynamical ranking in networks
Università di Genova（热那亚大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；African Institute for Mathematical Sciences（非洲数学科学研究所）；University of Colorado Boulder（科罗拉多大学博尔德分校）；BioFrontiers Institute（生物前沿研究所）；Santa Fe Institute（圣塔菲研究所）
Cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects in network dynamics. Focusing on cycle structure, this paper defines a new matrix, named cycle number matrix, to represent cycle information of a network, and an index, named cycle ratio, to quantify the node importance. Experiments on real networks suggest that cycle ratio contains rich information in addition to well-known benchmark indices, for example, the node rankings by cycle ratio are largely different from rankings by degree, H-index, coreness, betweenness and articulation ranking,…
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Kyung Hee University（庆熙大学）
Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest -- essential in determining reward or penalty -- is almost always an ambiguous task due to the incomplete nature of competition networks. Here we introduce ``Natural Ranking," a desirably unambiguous ranking method applicable to a complete (full) competition network, and formulate an analytical model …
We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network motifs. We show that the subgraph centrality (SC) can be obtained mathematically from the spectra of the adjacency matrix of the network. This measure is better able to discriminate the nodes of a network than alternate measures such as degree, closeness, betweenness and eigenvector centralities. We study eight real-world networks for which SC displays usef…
In this paper some results about the controllability of spectral centrality in a complex network are presented. In particular, the inverse problem of designing an unweigthed graph with a prescribed centrality is considered, by showing that for every possible ranking eventually with ties, an unweighted directed/undirected complex network can be found whose PageRank or eigenvector centrality gives the ranking considered. Different families of networks are presented in order to analytically solve this problem either for directed and undirected graphs with and without loops.
A deformation of the combinatorial Laplacian is proposed, consisting in a generalization of several existing Laplacians. As particular cases of this construction, the dilation Laplacians are shown to be useful tools for ranking in directed networks of pairwise comparisons. The eigenvector with the smallest eigenvalue of the dilation Laplacians has the same sign on any connected graph, and provides directly a ranking score of its nodes. The ranking method, phrased in terms of a group synchronization problem, is applied to artificial and real data, and its performance is compared with other rank…
