Showing papers on "Katz centrality published in 2016"

Identifying influential spreaders in complex networks based on gravity formula

Abstract: 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, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as synthetic networks. We also use the classical Susceptible–Infected–Recovered (SIR) epidemic model to verify the good performance of our method.

Identify influential spreaders in complex networks, the role of neighborhood

Abstract: 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 influential spreaders. Interestingly, we discover a saturation effect in considering the neighborhood of a node, which is not the case of the larger the better. Specifically speaking, considering the 2-step neighborhood of nodes is a good choice that balances the cost and performance. If further step of neighborhood is taken into consideration, there is no obvious improvement and even decrease in the ranking performance. The saturation effect may be informative for studies that make use of the local structure of a node to determine its importance in the network.

Locating influential nodes via dynamics-sensitive centrality.

Abstract: With great theoretical and practical significance, locating influential nodes of complex networks is a promising issue. In this paper, we present a dynamics-sensitive (DS) centrality by integrating 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 more accurate than degree, k-shell index and eigenvector centrality.

Stability and Continuity of Centrality Measures in Weighted Graphs

Abstract: This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable, whereas betweenness centrality is not. An alternative definition of the latter that preserves the same centrality notion while satisfying the stability criteria is introduced. Continuity is presented as a less stringent alternative to stability. Betweenness centrality is shown to be not only unstable but discontinuous. Numerical experiments in synthetic random networks and real-world data show that, in practice, stability and continuity imply different levels of robustness in the presence of noisy data. In particular, the stable betweenness centrality is shown to exhibit resilience against noise that is absent in the discontinuous and unstable standard betweenness centrality, while preserving a similar notion of centrality.

From Structure to Activity: Using Centrality Measures to Predict Neuronal Activity.

Abstract: It is clear that the topological structure of a neural network somehow determines the activity of the neurons within it. In the present work, we ask to what extent it is possible to examine the structural features of a network and learn something about its activity? Specifically, we consider how the centrality (the importance of a node in a network) of a neuron correlates with its firing rate. To investigate, we apply an array of centrality measures, including In-Degree, Closeness, Betweenness, Eigenvector, Katz, PageRank, Hyperlink-Induced Topic Search (HITS) and NeuronRank to Leaky-Integrate and Fire neural networks with different connectivity schemes. We find that Katz centrality is the best predictor of firing rate given the network structure, with almost perfect correlation in all cases studied, which include purely excitatory and excitatory–inhibitory networks, with either homogeneous connections or a small-world structure. We identify the properties of a network which will cause this correlation to...

Re-conceptualizing centrality in social networks†

Abstract: In the social sciences, networks are used to represent relationships between social actors, be they individuals or aggregates. The structural importance of these actors is assessed in terms of centrality indices which are commonly defined as graph invariants. Many such indices have been proposed, but there is no unifying theory of centrality. Previous attempts at axiomatic characterization have been focused on particular indices, and the conceptual frameworks that have been proposed alternatively do not lend themselves to mathematical treatment. We show that standard centrality indices, although seemingly distinct, can in fact be expressed in a common framework based on path algebras. Since, as a consequence, all of these indices preserve the neighbourhood-inclusion pre-order, the latter provides a conceptually clear criterion for the definition of centrality indices.

Assortativity Analysis of Real-World Network Graphs based on Centrality Metrics

Abstract: Assortativity index ( A. Index ) of real-world network graphs has been traditionally computed based on the degree centrality metric and the networks were classified as assortative, dissortative or neutral if the A. Index values are respectively greater than 0, less than 0 or closer to 0. In this paper, we evaluate the A. Index of real-world network graphs based on some of the commonly used centrality metrics (betweenness, eigenvector and closeness) in addition to degree centrality and observe that the assortativity classification of real-world network graphs depends on the node-level centrality metric used. We also propose five different levels of assortativity (strongly assortative, weakly assortative, neutral, weakly dissortative and strongly dissortative) for real-world networks and the corresponding range of A. Index value for the classification. We analyze a collection of 50 real-world network graphs with respect to each of the above four centrality metrics and estimate the empirical probability of observing a real-world network graph to exhibit a particular level of assortativity. We claim that a real-world network graph is more likely to be neutral with respect to the betweenness and degree centrality metrics and more likely to be assortative with respect to the eigenvector and closeness centrality metrics.

Matching exponential-based and resolvent-based centrality measures

Abstract: The relative importance of nodes in a network can be quantified via functions of the adjacency matrix. Two popular choices of function are the exponential, which is parameter-free, and the resolvent function, which yields the Katz centrality measure. Katz centrality can be the more computationally efficient, especially for large directed networks, and has the benefit of generalizing naturally to time-dependent network sequences, but it depends on a parameter. We give a prescription for selecting the Katz parameter based on the objective of matching the centralities of the exponential counterpart. For our new choice of parameter the resolvent can be very ill conditioned, but we argue that the centralities computed in floating point arithmetic can nevertheless reliably be used for ranking. Experiments on \revised{six} real networks show that the new choice of Katz parameter leads to rankings of nodes that \revised{generally} match those from the exponential centralities well in practice.

Combining fuzzy logic and eigenvector centrality measure in social network analysis

Abstract: The rapid growth of social networks use has made a great platform to present different services, increasing beneficiary of services and business profit. Therefore considering different levels of member activities in these networks, finding highly active members who can have the influence on the choice and the role of other members of the community is one the most important and challenging issues in recent years. These nodes that usually have a high number of relations with a lot of quality interactions are called influential nodes. There are various types of methods and measures presented to find these nodes. Among all the measures, centrality is the one that identifies various types of influential nodes in a network. Here we define four different factors which affect the strength of a relationship. A fuzzy inference system calculates the strength of each relation, creates a crisp matrix in which the corresponding elements identify the strength of each relation, and using this matrix eigenvector measure calculates the most influential node. Applying our suggested method resulted in choosing a more realistic central node with consideration of the strength of all friendships.

Centrality in the Global Network of Corporate Control

Abstract: Corporations across the world are highly interconnected in a large global network of corporate control. This paper investigates the global board interlock network, covering 400,000 firms linked through 1,700,000 edges representing shared directors between these firms. The main focus is on the concept of centrality, which is used to investigate the embeddedness of firms from a particular country within the global network. The study results in three contributions. First, to the best of our knowledge for the first time we can investigate the topology as well as the concept of centrality in corporate networks at a global scale, allowing for the largest cross-country comparison ever done in interlocking directorates literature. We demonstrate, amongst other things, extremely similar network topologies, yet large differences between countries when it comes to the relation between economic prominence indicators and firm centrality. Second, we introduce two new metrics that are specifically suitable for comparing the centrality ranking of a partition to that of the full network. Using the notion of centrality persistence we propose to measure the persistence of a partition's centrality ranking in the full network. In the board interlock network, it allows us to assess the extent to which the footprint of a national network is still present within the global network. Next, the measure of centrality ranking dominance tells us whether a partition (country) is more dominant at the top or the bottom of the centrality ranking of the full (global) network. Finally, comparing these two new measures of persistence and dominance between different countries allows us to classify these countries based the their embeddedness, measured using the relation between the centrality of a country's firms on the national and the global scale of the board interlock network.

Closeness centrality for networks with overlapping community structure

Abstract: Certain real-life networks have a community structure in which communities overlap. For example, a typical bus network includes bus stops (nodes), which belong to one or more bus lines (communities) that often overlap. Clearly, it is important to take this information into account when measuring the centrality of a bus stop—how important it is to the functioning of the network. For example, if a certain stop becomes inaccessible, the impact will depend in part on the bus lines that visit it. However, existing centrality measures do not take such information into account. Our aim is to bridge this gap. We begin by developing a new game-theoretic solution concept, which we call the Configuration semivalue, in order to have greater flexibility in modelling the community structure compared to previous solution concepts from cooperative game theory. We then use the new concept as a building block to construct the first extension of Closeness centrality to networks with community structure (overlapping or otherwise). Despite the computational complexity inherited from the Configuration semivalue, we show that the corresponding extension of Closeness centrality can be computed in polynomial time. We empirically evaluate this measure and our algorithm that computes it by analysing the Warsaw public transportation network.

Attachment Centrality: An Axiomatic Approach to Connectivity in Networks

Abstract: Centrality indices aim to quantify the importance of nodes or edges in a network. A number of new centrality indices have recently been proposed to try and capture the role of nodes in connecting the network. While these indices seem to deliver new insights, to date not enough is known about their theoretical properties. To address this issue, we propose an axiomatic approach. Specifically, we prove that there exists a unique centrality index satisfying some intuitive properties related to network connectivity. This new index, which we call Attachment Centrality, is equivalent to the Myerson value of a particular graph-restricted coalitional game. Building upon our theoretical analysis, we show that our Attachment Centrality has certain computational properties that are more attractive than the Myerson value for an arbitrary game.

Closeness Centrality for Networks with Overlapping Community Structure

Abstract: Certain real-life networks have a community structure in which communities overlap. For example, a typical bus network includes bus stops (nodes), which belong to one or more bus lines (communities) that often overlap. Clearly, it is important to take this information into account when measuring the centrality of a bus stop—how important it is to the functioning of the network. For example, if a certain stop becomes inaccessible, the impact will depend in part on the bus lines that visit it. However, existing centrality measures do not take such information into account. Our aim is to bridge this gap. We begin by developing a new game-theoretic solution concept, which we call the Configuration semivalue, in order to have greater flexibility in modelling the community structure compared to previous solution concepts from cooperative game theory. We then use the new concept as a building block to construct the first extension of Closeness centrality to networks with community structure (overlapping or otherwise). Despite the computational complexity inherited from the Configuration semivalue, we show that the corresponding extension of Closeness centrality can be computed in polynomial time. We empirically evaluate this measure and our algorithm that computes it by analysing the Warsaw public transportation network.

Identifying key papers within a journal via network centrality measures

Abstract: This article examines the extent to which existing network centrality measures can be used (1) as filters to identify a set of papers to start reading within a journal and (2) as article-level metrics to identify the relative importance of a paper within a journal. We represent a dataset of published papers in the Public Library of Science (PLOS) via a co-citation network and compute three established centrality metrics for each paper in the network: closeness, betweenness, and eigenvector. Our results show that the network of papers in a journal is scale-free and that eigenvector centrality (1) is an effective filter and article-level metric and (2) correlates well with citation counts within a given journal. However, closeness centrality is a poor filter because articles fit within a small range of citations. We also show that betweenness centrality is a poor filter for journals with a narrow focus and a good filter for multidisciplinary journals where communities of papers can be identified.

Identification of top-K influential communities in big networks

Abstract: Because communities are the fundamental component of big data/large data network graphs, community detection in large-scale graphs is an important area to study. Communities are a collection of a set of nodes with similar features. In a given graph there can be many features for clustering the nodes to form communities. Varying the features of interest can form several communities. Out of all communities that are formed, only a few communities are dominant and most influential for a given network graph. This might well contain influential nodes; i.e., for each possible feature of clustering, there will be only a few influential communities in the graph. Identification of such communities is a salient subject for research. This paper present a technique to identify the top-K communities, based on the average Katz centrality of all the communities in a network of communities and the distinctive nature of the communities. One can use these top-K communities to spread information efficiently into the network, as these communities are capable of influencing neighboring communities and thus spreading the information into the network efficiently.

Accelerating Computation of Distance Based Centrality Measures for Spatial Networks

Abstract: In this paper, by focusing on spatial networks embedded in the real space, we first extend the conventional step-based closeness and betweenness centralities by incorporating inter-nodes link distances obtained from the positions of nodes. Then, we propose a method for accelerating computation of these centrality measures by pruning some nodes and links based on the cut links of a given spatial network. In our experiments using spatial networks constructed from urban streets of cities of several types, our proposed method achieved about twice the computational efficiency compared with the baseline method. Actual amount of reduction in computation time depends on network structures. We further experimentally show by examining the highly ranked nodes that the closeness and betweenness centralities have completely different characteristics to each other.

Centrality and the dual-projection approach for two-mode social network data:

Abstract: Research using techniques from social network analysis have expanded dramatically in recent years. The availability of network data and the recognition that social network techniques can provide an...

Semantic Social Network Analysis Foresees Message Flows

Abstract: Social Network Analysis is employed widely as a means to compute the probability that a given message flows through a social network. This approach is mainly grounded upon the correct usage of three basic graph- theoretic measures: degree centrality, closeness centrality and betweeness centrality. We show that, in general, those indices are not adapt to foresee the flow of a given message, that depends upon indices based on the sharing of interests and the trust about depth in knowledge of a topic. We provide an extended model, that is a simplified version of a more general model already documented in the literature, the Semantic Social Network Analysis, and show that by means of this model it is possible to exceed the drawbacks of general indices discussed above.

Degree centrality, eigenvector centrality and the relation between them in Twitter

Abstract: In Social Media the directed links formed between the users, are used for the transfer of information. Based on previous research, the rate of information transfer in a social network depends on the strength of connections of the user in the network, which is measured by the centrality value. In this paper, based on data collected from Twitter, we perform an analysis of eigenvector centrality approach of finding the influential users. We investigate the variation in indegree and eigenvector centrality of users participating in a hashtag in Twitter, with respect to change in the amount of interactions. Here interactions are: tweets, mentions and replies. We also investigate the relationship between indegree and eigenvector centrality in a given hashtag. We make the following interesting observations. First, in Twitter, users with high eigenvector centrality need not be influential users. Second, in a given hashtag, there is an increase in users with both high indegree and eigenvector centrality when there are more user interactions. Here interactions are: tweets, mentions and replies, indicating both indegree and eigenvector centrality should be considered when finding influential users. Third, there is a positive correlation between indegree and eigenvector centrality.

Network topology and mean infection times

Abstract: A fundamental concept of social network analysis is centrality. Many analyses represent the network topology in terms of concept transmission/variation, e.g., influence, social structure, community or other aggregations. Even when the temporal nature of the network is considered, analysis is conducted at discrete points along a continuous temporal scale. Unfortunately, well-studied metrics of centrality do not take varying probabilities into account. The assumption that social and other networks that may be physically stationary, e.g., hard wired, are conceptually static in terms of information diffusion or conceptual aggregation (communities, etc.) can lead to incorrect conclusions. Our findings illustrate, both mathematically and experimentally, that if the notion of network topology is not stationary or fixed in terms of the concept, e.g., groups, belonging, community or other aggregations, centrality should be viewed probabilistically. We show through some surprising examples that study of transmission behavior based solely on a graph’s topological and degree properties is lacking when it comes to modeling network propagation or conceptual (vs. physical) structure.

Centrality analysis in PPI networks

Abstract: The need to investigate the atomic constituents of biological network has led to increasing popularity of topological studies. A biological network is a graphical representation of the interactome with nodes and edges. Therefore, graph theoretic measures can be applied to such networks. We have performed an empirical study comparing a number of centrality measures, viz., betweenness centrality, eigenvector centrality, pagerank centrality, closeness centrality and radiality associated with a graph in the context of PPI networks. This empirical study shows the superiority of pagerank and radiality measure. We believe that their superiority can be leveraged in the analysis of other networks such as gene networks or metabolic networks.

Edge Centrality via the Holevo Quantity

Abstract: In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann entropy of the graph. We show that this can be computed in terms of the Holevo quantity, a well known quantum information theoretical measure. While computing the Von Neumann entropy and hence the Holevo quantity requires computing the spectrum of the graph Laplacian, we show how to obtain a simplified measure through a quadratic approximation of the Shannon entropy. This in turns shows that the proposed centrality measure is strongly correlated with the negative degree centrality on the line graph. We evaluate our centrality measure through an extensive set of experiments on real-world as well as synthetic networks, and we compare it against commonly used alternative measures.