Showing papers on "Katz centrality published in 2019"

A Centrality Measure for Urban Networks Based on the Eigenvector Centrality Concept.

Abstract: A massive amount of information as geo-referenced data is now emerging from the digitization of contemporary cities. Urban streets networks are characterized by a fairly uniform degree distribution...

Optimal interlayer structure for promoting spreading of the susceptible-infected-susceptible model in two-layer networks.

Abstract: Real-world systems, ranging from social and biological to infrastructural, can be modeled by multilayer networks. Promoting spreading dynamics in multilayer networks may significantly facilitate electronic advertising and predicting popular scientific publications. In this study, we propose a strategy for promoting the spreading dynamics of the susceptible-infected-susceptible model by adding one interconnecting edge between two isolated networks. By applying a perturbation method to the discrete Markovian chain approach, we derive an index that estimates the spreading prevalence in the interconnected network. The index can be interpreted as a variant of Katz centrality, where the adjacency matrix is replaced by a weighted matrix with weights depending on the dynamical information of the spreading process. Edges that are less infected at one end and its neighborhood but highly infected at the other will have larger weights. We verify the effectiveness of the proposed strategy on small networks by exhaustively examining all latent edges and demonstrate that performance is optimal or near-optimal. For large synthetic and real-world networks, the proposed method always outperforms other static strategies such as connecting nodes with the highest degree or eigenvector centrality.

Centrality in Networks: Finding the Most Important Nodes

Abstract: Real networks are heterogeneous structures, with edges unevenly distributed among nodes, presenting community structure, motifs, transitivity, rich clubs, and other kinds of topological patterns. Consequently, the roles played by nodes in a network can differ greatly. For example, some nodes may be connectors between parts of the network, others may be central or peripheral, etc. The objective of this chapter is to describe how we can find the most important nodes in networks. The idea is to define a centrality measure for each node in the network, sort the nodes according to their centralities, and fix our attention to the first ranked nodes, which can be considered as the most relevant ones with respect to this centrality measure.

Centrality-Friendship Paradoxes: When Our Friends Are More Important Than Us

Abstract: The friendship paradox states that, on average, our friends have more friends than we do. In network terms, the average degree over the nodes can never exceed the average degree over the neighbours of nodes. This effect, which is a classic example of sampling bias, has attracted much attention in the social science and network science literature, with variations and extensions of the paradox being defined, tested and interpreted. Here, we show that a version of the paradox holds rigorously for eigenvector centrality: on average, our friends are more important than us. We then consider general matrix-function centrality, including Katz centrality, and give sufficient conditions for the paradox to hold. We also discuss which results can be generalized to the cases of directed and weighted edges. In this way, we add theoretical support for a field that has largely been evolving through empirical testing.

Network cartography of university students’ knowledge landscapes about the history of science: landmarks and thematic communities

Abstract: We examine students’ representations of their conceptions of the interlinked nature of science history and general history, as well as cultural history. Such knowledge landscapes of the history of science are explored by using the knowledge cartographic, network-based method of analysis to reveal the key items, landmarks, of the landscapes. We show that Katz centrality and Katz centrality efficiency are robust and reliable measures for finding landmarks. It is shown that landmarks are most often persons but include also colligatory landmarks, which refer to broader sets of events or ideas. By using Katz centrality we study how landmarks depend on periodisation of the networks to see what kinds of changes occur by changing the time window on history. The community structure of the networks is studied by using the Louvain method, to reveal the strong thematic dependence of the communities. When landmarks are studied in relation to community structure, it is found that colligatory landmarks gain importance in relation to person-centred landmarks. Network-based cartography thus reveals many features about landmarks, how communities emerge around them and how they depend on periodisation, which traditional methods can only detect or identify with difficulty. Such knowledge has direct impact on the design and planning of education and courses which could better address the need to facilitate a deeper understanding of the related nature of science history and history in general.

Trading, Profits, and Volatility in a Dynamic Information Network Model

Abstract: We introduce a dynamic noisy rational expectations model in which information diffuses through a general network of agents. In equilibrium, agents who are more closely connected have more similar period-by-period trades, and an agent’s profitability is determined by a centrality measure that is related to Katz centrality. Volatility after an information shock is more persistent in less central networks, and volatility and trading volume are also influenced by the network’s asymmetry and irregularity. Using account-level data of all portfolio holdings and trades on the Helsinki Stock Exchange between 1997 and 2003, we find support for the aggregate predictions, altogether suggesting that the market’s network structure is important for these dynamics.

Localization of eigenvector centrality in networks with a cut vertex.

Abstract: We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cut vertex Three distinct types of localization are identified in these structures One is related to the well-established hub node localization phenomenon and the other two are introduced and characterized here We gain insights into these problems by deriving the relationship between eigenvector centrality and Katz centrality This leads to an interpretation of the principal eigenvector as an approximation to more robust centrality measures which exist in the full span of an eigenbasis of the adjacency matrix

EpistasisRank and EpistasisKatz: interaction network centrality methods that integrate prior knowledge networks.

Abstract: Motivation An important challenge in gene expression analysis is to improve hub gene selection to enrich for biological relevance or improve classification accuracy for a given phenotype. In order to incorporate phenotypic context into co-expression, we recently developed an epistasis-expression network centrality method that blends the importance of gene-gene interactions (epistasis) and main effects of genes. Further blending of prior knowledge from functional interactions has the potential to enrich for relevant genes and stabilize classification. Results We develop two new expression-epistasis centrality methods that incorporate interaction prior knowledge. The first extends our SNPrank (EpistasisRank) method by incorporating a gene-wise prior knowledge vector. This prior knowledge vector informs the centrality algorithm of the inclination of a gene to be involved in interactions by incorporating functional interaction information from the Integrative Multi-species Prediction database. The second method extends Katz centrality to expression-epistasis networks (EpistasisKatz), extends the Katz bias to be a gene-wise vector of main effects and extends the Katz attenuation constant prefactor to be a prior-knowledge vector for interactions. Using independent microarray studies of major depressive disorder, we find that including prior knowledge in network centrality feature selection stabilizes the training classification and reduces over-fitting. Availability and implementation Methods and examples provided at https://github.com/insilico/Rinbix and https://github.com/insilico/PriorKnowledgeEpistasisRank. Supplementary information Supplementary data are available at Bioinformatics online.

Group Centrality Maximization for Large-scale Graphs.

Abstract: The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central group is $\mathcal{NP}$-hard. As a result, approximation algorithms to maximize group centralities were introduced recently. Despite a nearly-linear running time, approximation algorithms for group betweenness and (to a lesser extent) group closeness are rather slow on large networks due to high constant overheads. That is why we introduce GED-Walk centrality, a new submodular group centrality measure inspired by Katz centrality. In contrast to closeness and betweenness, it considers walks of any length rather than shortest paths, with shorter walks having a higher contribution. We define algorithms that (i) efficiently approximate the GED-Walk score of a given group and (ii) efficiently approximate the (proved to be $\mathcal{NP}$-hard) problem of finding a group with highest GED-Walk score. Experiments on several real-world datasets show that scores obtained by GED-Walk improve performance on common graph mining tasks such as collective classification and graph-level classification. An evaluation of empirical running times demonstrates that maximizing GED-Walk (in approximation) is two orders of magnitude faster compared to group betweenness approximation and for group sizes $\leq 100$ one to two orders faster than group closeness approximation. For graphs with tens of millions of edges, approximate GED-Walk maximization typically needs less than one minute. Furthermore, our experiments suggest that the maximization algorithms scale linearly with the size of the input graph and the size of the group.

Group Centrality Maximization for Large-scale Graphs.

Abstract: The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central group is $\mathcal{NP}$-hard. As a result, approximation algorithms to maximize group centralities were introduced recently. Despite a nearly-linear running time, approximation algorithms for group betweenness and (to a lesser extent) group closeness are rather slow on large networks due to high constant overheads. That is why we introduce GED-Walk centrality, a new submodular group centrality measure inspired by Katz centrality. In contrast to closeness and betweenness, it considers walks of any length rather than shortest paths, with shorter walks having a higher contribution. We define algorithms that (i) efficiently approximate the GED-Walk score of a given group and (ii) efficiently approximate the (proved to be $\mathcal{NP}$-hard) problem of finding a group with highest GED-Walk score. Experiments on several real-world datasets show that scores obtained by GED-Walk improve performance on common graph mining tasks such as collective classification and graph-level classification. An evaluation of empirical running times demonstrates that maximizing GED-Walk (in approximation) is two orders of magnitude faster compared to group betweenness approximation and for group sizes $\leq 100$ one to two orders faster than group closeness approximation. For graphs with tens of millions of edges, approximate GED-Walk maximization typically needs less than one minute. Furthermore, our experiments suggest that the maximization algorithms scale linearly with the size of the input graph and the size of the group.

Trip Centrality: walking on a temporal multiplex with non-instantaneous link travel time.

Abstract: In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their presence depends on time, and travelling between two nodes requires a non-vanishing time. Additionally, many networks are structured on several layers, representing, e.g., different transportation modes or service providers. Temporal generalisations of centrality metrics based on walk-counting, like Katz centrality, exist, however they do not account for non-zero link travel times and for the multiplex structure. We propose a generalisation of Katz centrality, termed Trip Centrality, counting only the walks that can be travelled according to the network temporal structure, i.e. "trips", while also differentiating the contributions of inter- and intra-layer walks to centrality. We show an application to the US air transport system, specifically computing airports' centrality losses due to delays in the flight network.

Trip Centrality: walking on a temporal multiplex with non-instantaneous link travel time

Abstract: In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their presence depends on time, and travelling between two nodes requires a non-vanishing time. Additionally, many networks are structured on several layers, representing, e.g., different transportation modes or service providers. Temporal generalisations of centrality metrics based on walk-counting, like Katz centrality, exist, however they do not account for non-zero link travel times and for the multiplex structure. We propose a generalisation of Katz centrality, termed Trip Centrality, counting only the paths that can be travelled according to the network temporal structure, i.e. "trips", while also differentiating the contributions of inter- and intra-layer walks to centrality. We show an application to the US air transport system, specifically computing airports' centrality losses due to delays in the flight network.

The neighborhood role in the linear threshold rank on social networks

Abstract: Centrality and influence spread are two of the most studied concepts in social network analysis. Several centrality measures, most of them, based on topological criteria, have been proposed and studied. In recent years new centrality measures have been defined inspired by the two main influence spread models, namely, the Independent Cascade Model (IC-model) and the Linear Threshold Model (LT-model). The Linear Threshold Rank (LTR) is defined as the total number of influenced nodes when the initial activation set is formed by a node and its immediate neighbors. It has been shown that LTR allows to rank influential actors in a more distinguishable way than other measures like the PageRank, the Katz centrality, or the Independent Cascade Rank. In this paper we propose a generalized LTR measure that explore the sensitivity of the original LTR, with respect to the distance of the neighbors included in the initial activation set. We appraise the viability of the approach through different case studies. Our results show that by using neighbors at larger distance, we obtain rankings that distinguish better the influential actors. However, the best differentiating ranks correspond to medium distances. Our experiments also show that the rankings obtained for the different levels of neighborhood are not highly correlated, which validates the measure generalization.

Centralities for Networks with Consumable Resources

Abstract: Identification of influential nodes is an important step in understanding and controlling the dynamics of information, traffic, and spreading processes in networks. As a result, a number of centrality measures have been proposed and used across different application domains. At the heart of many of these measures lies an assumption describing the manner in which traffic (of information, social actors, particles, etc.) flows through the network. For example, some measures only count shortest paths while others consider random walks. This paper considers a spreading process in which a resource necessary for transit is partially consumed along the way while being refilled at special nodes on the network. Examples include fuel consumption of vehicles together with refueling stations, information loss during dissemination with error-correcting nodes, and consumption of ammunition of military troops while moving. We propose generalizations of the well-known measures of betweenness, random-walk betweenness, and Katz centralities to take such a spreading process with consumable resources into account. In order to validate the results, experiments on real-world networks are carried out by developing simulations based on well-known models such as Susceptible-Infected-Recovered and congestion with respect to particle hopping from vehicular flow theory. The simulation-based models are shown to be highly correlated with the proposed centrality measures.Reproducibility: Our code and experiments are available at https://github.com/hmwesigwa/soc_centrality

Sampling Based Katz Centrality Estimation for Large-Scale Social Networks

Abstract: Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network is unpractical and computationally expensive. In this paper, we propose a novel method to estimate Katz centrality based on graph sampling techniques. Specifically, we develop an unbiased estimator for Katz centrality using a multi-round sampling approach. We further propose SAKE, a Sampling based Algorithm for fast Katz centrality Estimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. The computational complexity of SAKE is much lower than the state-of-the-arts. Extensive evaluation experiments based on four real world networks show that the proposed algorithm achieves low mean relative error with low sampling rate, and it works well in identifying high influence vertices in social networks.

Potential gain as a centrality measure

Abstract: Navigability is a distinctive features of graphs associated with artificial or natural systems whose primary goal is the transportation of information or goods. We say that a graph G is navigable when an agent is able to efficiently reach any target node in G by means of local routing decisions. In a social network navigability translates to the ability of reaching an individual through personal contacts. Graph navigability is well-studied, but a fundamental question is still open: why are some individuals more likely than others to be reached via short, friend-of-a-friend, communication chains? In this article we answer the question above by proposing a novel centrality metric called the potential gain, which, in an informal sense, quantifies the easiness at which a target node can be reached. We define two variants of the potential gain, called the geometric and the exponential potential gain, and present fast algorithms to compute them. The geometric and the potential gain are the first instances of a novel class of composite centrality metrics, i.e., centrality metrics which combine the popularity of a node in G with its similarity to all other nodes. As shown in previous studies, popularity and similarity are two main criteria which regulate the way humans seek for information in large networks such as Wikipedia. We give a formal proof that the potential gain of a node is always equivalent to the product of its degree centrality (which captures popularity) and its Katz centrality (which captures similarity). CCS CONCEPTS • Information systems → Web crawling; Web indexing.

Concurrent Katz Centrality for Streaming Graphs

Abstract: Most current frameworks for streaming graph analysis “stop the world” and halt ingesting data while updating analysis results. Others add overhead for different forms of version control. In both methods, adding additional analysis kernels adds additional overhead to the entire system. A new formal model of concurrent analysis lets some algorithms, those valid for the model, update results concurrently with data ingest without synchronization. Additional kernels incur very little overhead. Here we present the first experimental results for the new model, considering the performance and result latency of updating Katz centrality on a low-power edge platform. The Katz centrality values remain close to the synchronous algorithm while reducing latency delay from 12.8$\times $ to 179$\times $.

Community Detection via Katz and Eigenvector Centrality.

Abstract: The computational demands of community detection algorithms such as Louvain and spectral optimization can be prohibitive for large networks. Eigenvector centrality and Katz centrality are two network statistics commonly used to describe the relative importance of nodes; and their calculation can be closely approximated on large networks by scalable iterative methods. In this paper, we present and leverage a surprising relationship between Katz centrality and eigenvector centrality to detect communities. Beyond the computational gains, we demonstrate that our approach identifies communities that are as good or better than conventional methods.

A Trust Model for Evaluating Trust and Centrality Based on Entropy Weight Method in Social Commerce

Abstract: Trust of the nodes plays an important role in users’ purchase decisions and trusted nodes can influence other nodes in the social commerce. The evaluation and prediction of users’ trustworthiness is also of great importance for social commerce marketing and promotion. However, analysis of trust and detection of what factors influence trust between users need investigation. This paper proposes a trust model and divides trust into direct trust and indirect trust which presented in the form of familiarity trust, similarity trust, prestige trust and ability trust. The respective weights of four attributes are calculated through entropy weight method. Different centrality approaches such as Eigenvector Centrality, PageRank and Katz Centrality are used to find influential nodes. We found similarity and prestige is relatively more important than familiarity and ability trust in users’ connections. Besides, there is a strong linear relationship between user nodes’ trust and their centrality.