Showing papers on "Katz centrality published in 2017"

Degree Centrality, Betweenness Centrality, and Closeness Centrality in Social Network

Abstract: Social network theory is becoming more and more significant in social science, and the centrality measure is underlying this burgeoning theory. In perspective of social network, individuals, organizations, companies etc. are like nodes in the network, and centrality is used to measure these nodes’ power, activity, communication convenience and so on. Meanwhile, degree centrality, betweenness centrality and closeness centrality are the popular detailed measurements. This paper presents these 3 centrality in-depth, from principle to algorithm, and prospect good in the future use. Keywordssocial network; centrality; degree centrality; betweenness centrality; closeness centrality

Centrality Measures in Networks

Abstract: We show that although the prominent centrality measures in network analysis make use of different information about nodes' positions, they all process that information in an identical way: they all spring from a common family that are characterized by the same simple axioms. In particular, they are all based on a monotonic and additively separable treatment of a statistic that captures a node's position in the network.

A novel weight neighborhood centrality algorithm for identifying influential spreaders in complex networks

Abstract: Identifying the most influential spreaders in complex networks is crucial for optimally using the network structure and designing efficient strategies to accelerate information dissemination or prevent epidemic outbreaks. In this paper, by taking into account the centrality of a node and its neighbors’ centrality which depends on the diffusion importance of links, we propose a novel influence measure, the weight neighborhood centrality, to quantify the spreading ability of nodes in complex networks. To evaluate the performance of our method, we use the Susceptible–Infected–Recovered (SIR) model to simulate the epidemic spreading process on six real-world networks and four artificial networks. By measuring the rank imprecision and the rank correlation between the rank lists generated by simulation results via SIR and the ones generated by centrality measures, it shows that in general the weight neighborhood centrality can rank the spreading ability of nodes more accurately than its benchmark centrality, especially when using the degree k or coreness k s as the benchmark centrality. Further, we compare the monotonicity and the computational complexity of different ranking methods, which show that our method not only can be better at distinguishing the spreading ability of nodes but also can be used in large-scale networks due to the high computation efficiency.

Identification of top-K nodes in large networks using Katz centrality

Abstract: Network theory concepts form the core of algorithms that are designed to uncover valuable insights from various datasets. Especially, network centrality measures such as Eigenvector centrality, Katz centrality, PageRank centrality etc., are used in retrieving top-K viral information propagators in social networks,while web page ranking in efficient information retrieval, etc. In this paper, we propose a novel method for identifying top-K viral information propagators from a reduced search space. Our algorithm computes the Katz centrality and Local average centrality values of each node and tests the values against two threshold (constraints) values. Only those nodes, which satisfy these constraints, form the search space for top-K propagators. Our proposed algorithm is tested against four datasets and the results show that the proposed algorithm is capable of reducing the number of nodes in search space at least by 70%. We also considered the parameter ( $$\alpha$$ and $$\beta$$ ) dependency of Katz centrality values in our experiments and established a relationship between the $$\alpha$$ values, number of nodes in search space and network characteristics. Later, we compare the top-K results of our approach against the top-K results of degree centrality.

How to Identify the Most Powerful Node in Complex Networks? A Novel Entropy Centrality Approach

Abstract: Centrality is one of the most studied concepts in network analysis. Despite an abundance of methods for measuring centrality in social networks has been proposed, each approach exclusively characterizes limited parts of what it implies for an actor to be “vital” to the network. In this paper, a novel mechanism is proposed to quantitatively measure centrality using the re-defined entropy centrality model, which is based on decompositions of a graph into subgraphs and analysis on the entropy of neighbor nodes. By design, the re-defined entropy centrality which describes associations among node pairs and captures the process of influence propagation can be interpreted explained as a measure of actor potential for communication activity. We evaluate the efficiency of the proposed model by using four real-world datasets with varied sizes and densities and three artificial networks constructed by models including Barabasi-Albert, Erdos-Renyi and Watts-Stroggatz. The four datasets are Zachary’s karate club, USAir97, Collaboration network and Email network URV respectively. Extensive experimental results prove the effectiveness of the proposed method.

Street network analysis "edge effects": examining the sensitivity of centrality measures to boundary conditions

Abstract: With increased interest in the use of network analysis to study the urban and regional environment, it is important to understand the sensitivity of centrality analysis results to the so-called “edge effect”. Most street network models have artificial boundaries, and there are principles that can be applied to minimise or eliminate the effect of the boundary condition. However, the extent of this impact has not been systematically studied and remains little understood. In this article we present an empirical study on the impact of different network model boundaries on the results of closeness and betweenness centrality analysis of street networks. The results demonstrate that the centrality measures are affected differently by the edge effect, and that the same centrality measure is affected differently depending on the type of network distance used. These results highlight the importance, in any study of street networks, of defining the network's boundary in a way that is relevant to the research question, and of selecting appropriate analysis parameters and statistics.

Make a difference: Diversity-driven social mobile crowdsensing

Abstract: In a mobile crowdsensing (MCS) application, user diversity and social effect are two important phenomena that determine its profitability, where the former improves the sensing quality, while the latter incentives the users' participation. In this paper, we consider a reward mechanism design for the service provider to achieve diversity in the collected data by exploiting the users' social relationship. Specifically, we formulate a two-stage decision problem, where the service provider first optimizes its rewards for profit maximization. The users then decide their effort levels through social network interactions as a participation game. The analysis is particularly challenging due to the users' interplay in both the diversity and social graphs, which leads to a non-convex bilevel optimization problem. Surprisingly, we find that the service provider can focus on one superimposed graph that incorporates the diversity and social relationship and compute the optimal reward as the Katz centrality in closed-form. Simulation results, based on the random graph and a real Facebook trace, show that the availability of network information improves both the service provider's profit and the users' social surplus over the incomplete information cases.

Node and layer eigenvector centralities for multiplex networks

Abstract: Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover, several efficient computational tools are available for their computation. Moving up in dimensionality, several efforts have been made in the past to describe an eigenvector-based centrality measure that generalizes Bonacich index to the case of multiplex networks. In this work, we propose a new definition of eigenvector centrality that relies on the Perron eigenvector of a multi-homogeneous map defined in terms of the tensor describing the network. We prove that existence and uniqueness of such centrality are guaranteed under very mild assumptions on the multiplex network. Extensive numerical studies are proposed to test the newly introduced centrality measure and to compare it to other existing eigenvector-based centralities.

Evaluating Influential Nodes in Social Networks by Local Centrality with a Coefficient

Abstract: Influential nodes are rare in social networks, but their influence can quickly spread to most nodes in the network. Identifying influential nodes allows us to better control epidemic outbreaks, accelerate information propagation, conduct successful e-commerce advertisements, and so on. Classic methods for ranking influential nodes have limitations because they ignore the impact of the topology of neighbor nodes on a node. To solve this problem, we propose a novel measure based on local centrality with a coefficient. The proposed algorithm considers both the topological connections among neighbors and the number of neighbor nodes. First, we compute the number of neighbor nodes to identify nodes in cluster centers and those that exhibit the “bridge” property. Then, we construct a decreasing function for the local clustering coefficient of nodes, called the coefficient of local centrality, which ranks nodes that have the same number of four-layer neighbors. We perform experiments to measure node influence on both real and computer-generated networks using six measures: Degree Centrality, Betweenness Centrality, Closeness Centrality, K-Shell, Semi-local Centrality and our measure. The results show that the rankings obtained by the proposed measure are most similar to those of the benchmark Susceptible-Infected-Recovered model, thus verifying that our measure more accurately reflects the influence of nodes than do the other measures. Further, among the six tested measures, our method distinguishes node influence most effectively.

Hierarchical Decomposition for Betweenness Centrality Measure of Complex Networks.

Abstract: Betweenness centrality is an indicator of a node's centrality in a network. It is equal to the number of shortest paths from all vertices to all others that pass through that node. Most of real-world large networks display a hierarchical community structure, and their betweenness computation possesses rather high complexity. Here we propose a new hierarchical decomposition approach to speed up the betweenness computation of complex networks. The advantage of this new method is its effective utilization of the local structural information from the hierarchical community. The presented method can significantly speed up the betweenness calculation. This improvement is much more evident in those networks with numerous homogeneous communities. Furthermore, the proposed method features a parallel structure, which is very suitable for parallel computation. Moreover, only a small amount of additional computation is required by our method, when small changes in the network structure are restricted to some local communities. The effectiveness of the proposed method is validated via the examples of two real-world power grids and one artificial network, which demonstrates that the performance of the proposed method is superior to that of the traditional method.

Graph Manipulations for Fast Centrality Computation

Abstract: The betweenness and closeness metrics are widely used metrics in many network analysis applications. Yet, they are expensive to compute. For that reason, making the betweenness and closeness centrality computations faster is an important and well-studied problem. In this work, we propose the framework BADIOS that manipulates the graph by compressing it and splitting into pieces so that the centrality computation can be handled independently for each piece. Experimental results show that the proposed techniques can be a great arsenal to reduce the centrality computation time for various types and sizes of networks. In particular, it reduces the betweenness centrality computation time of a 4.6 million edges graph from more than 5 days to less than 16 hours. For the same graph, the closeness computation time is decreased from more than 3 days to 6 hours (12.7x speedup).

Identification of influential nodes in complex networks: Method from spreading probability viewpoint

Abstract: The problem of identifying influential nodes in complex networks has attracted much attention owing to its wide applications, including how to maximize the information diffusion, boost product promotion in a viral marketing campaign, prevent a large scale epidemic and so on. From spreading viewpoint, the probability of one node propagating its information to one other node is closely related to the shortest distance between them, the number of shortest paths and the transmission rate. However, it is difficult to obtain the values of transmission rates for different cases, to overcome such a difficulty, we use the reciprocal of average degree to approximate the transmission rate. Then a semi-local centrality index is proposed to incorporate the shortest distance, the number of shortest paths and the reciprocal of average degree simultaneously. By implementing simulations in real networks as well as synthetic networks, we verify that our proposed centrality can outperform well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, k-shell centrality, and nonbacktracking centrality. In particular, our findings indicate that the performance of our method is the most significant when the transmission rate nears to the epidemic threshold, which is the most meaningful region for the identification of influential nodes.

Finding groups with maximum betweenness centrality

Abstract: In this paper we consider the problem of identifying the most influential or centralgroup of nodes of some predefined size in a network. Such a group has the largest value of betweenness centrality or one of its variants, for example, the length-scaled or the bounded-distance betweenness centralities. We demonstrate that this problem can be modelled as a mixed integer program MIP that can be solved for reasonably sized network instances using off-the-shelf MIP solvers. We also discuss interesting relations between the group betweenness and the bounded-distance betweenness centrality concepts. In particular, we exploit these relations in an algorithmic scheme to identify approximate solutions for the original problem of identifying the most central group of nodes. Furthermore, we generalize our approach for identification of not only the most central groups of nodes, but also central groups of graph elements that consists of either nodes or edges exclusively, or their combination according to some pre-specified criteria. If necessary, additional cohesiveness properties can also be enforced, for example, the targeted group should form a clique or a κ-club. Finally, we conduct extensive computational experiments with different types of real-life and synthetic network instances to show the effectiveness and flexibility of the proposed framework. Even more importantly, our experiments reveal some interesting insights into the properties of influential groups of graph elements modelled using the maximum betweenness centrality concept or one of its variations.

A computationally lightweight and localized centrality metric in lieu of betweenness centrality for complex network analysis

Abstract: The betweenness centrality (BWC) of a vertex is a measure of the fraction of shortest paths between any two vertices going through the vertex and is one of the widely used shortest path-based centrality metrics for the complex network analysis. However, it takes O($$\vert V\vert ^{2}+\vert V\vert \vert E\vert )$$|V|2+|V||E|) time (where V and E are, respectively, the sets of nodes and edges of a network graph) to compute the BWC of just a single node. Our hypothesis is that nodes with a high degree, but low local clustering coefficient, are more likely to be on the shortest paths of several node pairs and are likely to incur a larger BWC value. Accordingly, we define the local clustering coefficient-based degree centrality (LCCDC) for a node as the product of the degree centrality of the node and one minus the local clustering coefficient of the node. The LCCDC of a node can be computed based on just the knowledge of the two-hop neighborhood of a node and would take significantly lower time. We conduct an exhaustive correlation analysis and observe the LCCDC to incur the largest correlation coefficient values with BWC (compared to other centrality metrics under three different correlation measures) and to hold very strong levels of positive correlation with BWC for at least 14 of the 18 real-world networks analyzed. Hence, we claim the LCCDC to be an apt metric to rank the nodes or compare any two nodes of a real-world network graph in lieu of BWC.

Centrality of regions in R&D networks: a new measurement approach using the concept of bridging paths

Abstract: Centrality of regions in RD its relative outward orientation in terms of all established links; and its diversification of R&D collaborations among partner regions. The measure and its behaviour with respect to other conventional centrality mea...

Graph Ranking Guarantees for Numerical Approximations to Katz Centrality

Abstract: Graphs and networks are prevalent in modeling relational datasets from many fields of research. By using iterative solvers to approximate graph measures (specifically Katz Centrality), we can obtain a ranking vector consisting of a number for each vertex in the graph identifying its relative importance. We use the residual to accurately estimate how much of the ranking from an approximate solution matches the ranking given by the exact solution. Using probabilistic matrix norms and applying numerical analysis to the computation of Katz Centrality, we obtain bounds on the accuracy of the approximation compared to the exact solution with respect to the highly ranked nodes. This relates the numerical accuracy of the linear solver to the data analysis accuracy of finding the correct ranking. In particular, we answer the question of which pairwise rankings are reliable given an approximate solution to the linear system. Experiments on many real-world networks up to several million vertices and several hundred million edges validate our theory and show that we are able to accurately estimate large portions of the approximation. By analyzing convergence error, we develop confidence in the ranking schemes of data mining.

Interplay between Social Influence and Network Centrality: A Comparative Study on Shapley Centrality and Single-Node-Influence Centrality

Abstract: We study network centrality based on dynamic influence propagation models in social networks To illustrate our integrated mathematical-algorithmic approach for understanding the fundamental interplay between dynamic influence processes and static network structures, we focus on two basic centrality measures: (a) Single Node Influence (SNI) centrality, which measures each node's significance by its influence spread; and (b) Shapley Centrality, which uses the Shapley value of the influence spread function --- formulated based on a fundamental cooperative-game-theoretical concept --- to measure the significance of nodes We present a comprehensive comparative study of these two centrality measures Mathematically, we present axiomatic characterizations, which precisely capture the essence of these two centrality measures and their fundamental differences Algorithmically, we provide scalable algorithms for approximating them for a large family of social-influence instances Empirically, we demonstrate their similarity and differences in a number of real-world social networks, as well as the efficiency of our scalable algorithms Our results shed light on their applicability: SNI centrality is suitable for assessing individual influence in isolation while Shapley centrality assesses individuals' performance in group influence settings

A Dynamic Algorithm for Updating Katz Centrality in Graphs

Abstract: Many large datasets from a variety of fields of research can be represented as graphs. A common query is to identify the most important, or highly ranked, vertices in a graph. Centrality metrics are used to obtain numerical scores for each vertex in the graph. The scores can then be translated to rankings identifying relative importance of vertices. In this work we focus on Katz Centrality, a linear algebra based metric. In many real applications, since data is constantly being produced and changed, it is necessary to have a dynamic algorithm to update centrality scores with minimal computation when the graph changes. We present an algorithm for updating Katz Centrality scores in a dynamic graph that incrementally updates the centrality scores as the underlying graph changes. Our proposed method exploits properties of iterative solvers to obtain updated Katz scores in dynamic graphs. Our dynamic algorithm improves performance and achieves speedups of over two orders of magnitude compared to a standard static algorithm while maintaining high quality of results.

GFT centrality: A new node importance measure for complex networks

Abstract: Identifying central nodes is very crucial to design efficient communication networks or to recognize key individuals of a social network. In this paper, we introduce Graph Fourier Transform Centrality (GFT-C), a metric that incorporates local as well as global characteristics of a node, to quantify the importance of a node in a complex network. GFT-C of a reference node in a network is estimated from the GFT coefficients derived from the importance signal of the reference node. Our study reveals the superiority of GFT-C over traditional centralities such as degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, and Google PageRank centrality, in the context of various arbitrary and real-world networks with different degree–degree correlations.

Attachment Centrality for Weighted Graphs

Abstract: Measuring how central nodes are in terms of connecting a network has recently received increasing attention in the literature. While a few dedicated centrality measures have been proposed, Skibski et al. [2016] showed that the Attachment Centrality is the only one that satisfies certain natural axioms desirable for connectivity. Unfortunately, the Attachment Centrality is defined only for unweighted graphs which makes this measure ill-fitted for various applications. For instance, covert networks are typically weighted, where the weights carry additional intelligence available about criminals or terrorists and the links between them. To analyse such settings, in this paper we extend the Attachment Centrality to node-weighted and edgeweighted graphs. By an axiomatic analysis, we show that the Attachment Centrality is closely related to the Degree Centrality in weighted graphs.

Axiomatic Characterization of Game-Theoretic Network Centralities

Abstract: One of the fundamental research challenges in network science is the centrality analysis, i.e., identifying the nodes that play the most important roles in the network. In this paper, we focus on the game-theoretic approach to centrality analysis. While various centrality indices have been proposed based on this approach, it is still unknown what distinguishes this family of indices from the more classical ones. In this paper, we answer this question by providing the first axiomatic characterization of game-theoretic centralities. Specifically, we show that every centrality can be obtained following the game-theoretic approach, and show that two natural classes of game-theoretic centrality can be characterized by two intuitive properties pertaining to Myerson's notion of Fairness.

Computing Top-k Closeness Centrality in Fully-dynamic Graphs

Abstract: Closeness is a widely-studied centrality measure. Since it requires all pairwise distances, computing closeness for all nodes is infeasible for large real-world networks. However, for many applications, it is only necessary to find the k most central nodes and not all closeness values. Prior work has shown that computing the top-k nodes with highest closeness can be done much faster than computing closeness for all nodes in real-world networks. However, for networks that evolve over time, no dynamic top-k closeness algorithm exists that improves on static recomputation. In this paper, we present several techniques that allow us to efficiently compute the k nodes with highest (harmonic) closeness after an edge insertion or an edge deletion. Our algorithms use information obtained during earlier computations to omit unnecessary work. However, they do not require asymptotically more memory than the static algorithms (i. e., linear in the number of nodes). We propose separate algorithms for complex networks (which exhibit the small-world property) and networks with large diameter such as street networks, and we compare them against static recomputation on a variety of real-world networks. On many instances, our dynamic algorithms are two orders of magnitude faster than recomputation; on some large graphs, we even reach average speedups between $10^3$ and $10^4$.

The Node Influence Analysis in Social Networks Based on Structural Holes and Degree Centrality

Abstract: The analysis of node influence plays important role in product marketing, public opinion analysis, disease transmission and other fields. Researchers have proposed a variety of methods to measure node influence, with the rapid expansion of the scale of social networks, Degree Centrality algorithm attracts much attention for its lowest time complexity, however, its result is not sufficiently accurate because it considers only the local node information and not reflects the impact of topological connections among neighbor nodes. To solve this problem, we proposed a novel measure based on Structural Holes and Degree Centrality(SHDC). Our measure combines Structural Hole and Degree Centrality to measure the node influence. It uses Degree Centrality to make a fast and coarse distinction between the influence of nodes and uses Structure Hole to reflect the impact of topological connections among neighbor nodes, which improves the ability to distinguish the influence of nodes in the low time complexity. Experimental results show that the SHDC algorithm can more accurately measure the influence of nodes than Degree Centrality and Structural Hole and it has stronger applicability.

Ranking the key nodes with temporal degree deviation centrality on complex networks

Abstract: Records of time-stamped social interactions between pairs of individuals (e.g. the human contact networks involved in the transmission of disease, ad hoc radio networks between moving vehicles, and the transactions between principals in a market) constitute a so-called temporal network. A remarkable difference between temporal networks and conventional static networks is that time-stamped events rather than links are the unit elements generating the collective behavior of nodes. While we have good centralities to measure the importance of the nodes in static networks, so far these have been lacking for temporal cases. In this paper we propose a simple but powerful centrality, the degree deviation centrality, which calculates the deviation of temporal degree centrality. This enables us to extend network properties vertex degree centrality metrics in a very natural way to the temporal case. We then demonstrate how our centrality applies to identify the vital nodes in temporal networks by epidemic spreading dynamics based on SI (susceptible-infected) model. The numerical experiments on several real networks indicate that the temporal degree deviation centrality method outperforms some other indicators, and the results with different time window size show that the improvement is also robust.

Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach

Abstract: Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition.

Approximating Personalized Katz Centrality in Dynamic Graphs

Abstract: Dynamic graphs can capture changing relationships in many real datasets that evolve over time. One of the most basic questions about networks is the identification of the “most important” vertices in a network. Measures of vertex importance called centrality measures are used to rank vertices in a graph. In this work, we focus on Katz Centrality. Typically, scores are calculated through linear algebra but in this paper we present an new alternative, agglomerative method of calculating Katz scores and extend it for dynamic graphs. We show that our static algorithm is several orders of magnitude faster than the typical linear algebra approach while maintaining good quality of the scores. Furthermore, our dynamic graph algorithm is faster than pure static recomputation every time the graph changes and maintains high recall of the highly ranked vertices on both synthetic and real graphs.