Airport centrality analysis: The Azores archipelago case

Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.

Functional magnetic resonance data acquired in a task-absent condition (“resting state”) require new data analysis techniques that do not depend on an activation model. In this work, we introduce an alternative assumption- and parameter-free method based on a particular form of node centrality called eigenvector centrality. Eigenvector centrality attributes a value to each voxel in the brain such that a voxel receives a large value if it is strongly correlated with many other nodes that are themselves central within the network. Google's PageRank algorithm is a variant of eigenvector centrality. Thus far, other centrality measures - in particular “betweenness centrality” - have been applied to fMRI data using a pre-selected set of nodes consisting of several hundred elements. Eigenvector centrality is computationally much more efficient than betweenness centrality and does not require thresholding of similarity values so that it can be applied to thousands of voxels in a region of interest covering the entire cerebrum which would have been infeasible using betweenness centrality. Eigenvector centrality can be used on a variety of different similarity metrics. Here, we present applications based on linear correlations and on spectral coherences between fMRI times series. This latter approach allows us to draw conclusions of connectivity patterns in different spectral bands. We apply this method to fMRI data in task-absent conditions where subjects were in states of hunger or satiety. We show that eigenvector centrality is modulated by the state that the subjects were in. Our analyses demonstrate that eigenvector centrality is a computationally efficient tool for capturing intrinsic neural architecture on a voxel-wise level.

Principal eigenvector localization and centrality in networks: Revisited

هدف: هدف از پژوهش حاضر بررسی میزان مرکزیت شبکه اجتماعی هم‌نویسندگی موجود در بین مجلات علم اطلاعات نمایه شده در پایگاهتامسون رویترز می باشد. روش‌شناسی:پژوهش حاضر با استفاده از روش تحلیل شبکه ای صورت گرفته است. جامعه پژوهش تمامی مجلات علم اطلاعات است که دارای ضریب تأثیرگذاری بالاتر از 6/0 می باشند. یافته ها: نتایج حاصل از تحلیل نشان داد که گلنزل بالاترین مرکزیت رتبه، بینابینی، بردار ویژه و نزدیکی را در مجله علم‌سنجی دارد و نیکولاس بالاترین مرکزیت رتبه، بردار ویژه و مرکزیت بتا را در مجله علوم اطلاعات دارد. نتایج حاکی از آن است که به طور کلی شبکه اجتماعی هم‌نویسندگی پژوهشگران علم اطلاعات کم تراکممی باشد و از لحاظ سنجه های مرکزیت در مقایسه با سایر رشته های علمی در سطح پایین‌تری قرار دارد.

Today, there exist many centrality measures for assessing the importance of nodes in a network as a function of their position and the underlying topology. One class of such measures builds on eigenvector centrality, where the importance of a node is derived from the importance of its neighboring nodes. For directed and weighted complex networks, where the nodes can carry some intrinsic property value, there have been centrality measures proposed that are variants of eigenvector centrality. However, these expressions all suffer from shortcomings. Here, an extension of such centrality measures is presented that remedies all previously encountered issues. While similar improved centrality measures have been proposed as algorithmic recipes, the novel quantity that is presented here is a purely analytical expression, only utilizing the adjacency matrix and the vector of node values. The derivation of the new centrality measure is motivated in detail. Specifically, the centrality itself is ideal for the analysis of directed and weighted networks (with node properties) displaying a bow-tie topology. The novel bow-tie centrality is then computed for a unique and extensive real-world dataset, coming from economics. It is shown how the bow-tie centrality assesses the relevance of nodes similarly to other eigenvector centrality measures, while not being plagued by their drawbacks in the presence of cycles in the network.

Purpose Understanding the types of individuals and their position in the network may improve interventions for people who inject drugs (PWID). Methods From the Transmission Reduction Intervention Project (TRIP), which enrolled PWID and their contacts in Athens, Greece, from 2013 to 2015, we extracted the largest connected component of the network (i.e., the largest group of connected individuals) and identified members who were in the top quartile of the distribution for three network centrality measures: closeness, betweenness, and eigenvector. Using logistic regression, we evaluated associations between high centrality measures and individual sociodemographic characteristics and behaviors. We also varied the definition for high centrality. Results Among 231 individuals, 80% were male and between the ages of 25-40 years. Over half of the individuals injected at least once per day, compared to less than daily. Individuals who injected at least once per day were more likely to have high closeness (odds ratio (OR) = 3.36; 95% confidence interval (CI) = 1.57, 8.42), high betweenness (OR = 2.22; 95% CI = 1.06, 4.67), and eigenvector centrality (OR = 4.50; 95% CI = 1.89,10.68). Individuals who engaged in sex without a condom were less likely to have high closeness (OR = 0.18; 95% CI = 0.07, 0.45) or eigenvector (OR = 0.19; 95% CI = 0.07, 0.49) centrality. Conclusions Individual characteristics and behaviors were associated with centrality and may impact an individual’s position in the network. These associations could be useful in identifying important community members to engage as part of public health initiatives.

The two-steps eigenvector centrality in complex networks

BackgroundLiving systems are associated with Social networks — networks made up of nodes, some of which may be more important in various aspects as compared to others. While different quantitative measures labeled as “centralities” have previously been used in the network analysis community to find out influential nodes in a network, it is debatable how valid the centrality measures actually are. In other words, the research question that remains unanswered is: how exactly do these measures perform in the real world? So, as an example, if a centrality of a particular node identifies it to be important, is the node actually important?PurposeThe goal of this paper is not just to perform a traditional social network analysis but rather to evaluate different centrality measures by conducting an empirical study analyzing exactly how do network centralities correlate with data from published multidisciplinary network data sets.MethodWe take standard published network data sets while using a random network to establish a baseline. These data sets included the Zachary's Karate Club network, dolphin social network and a neural network of nematode Caenorhabditis elegans. Each of the data sets was analyzed in terms of different centrality measures and compared with existing knowledge from associated published articles to review the role of each centrality measure in the determination of influential nodes.ResultsOur empirical analysis demonstrates that in the chosen network data sets, nodes which had a high Closeness Centrality also had a high Eccentricity Centrality. Likewise high Degree Centrality also correlated closely with a high Eigenvector Centrality. Whereas Betweenness Centrality varied according to network topology and did not demonstrate any noticeable pattern. In terms of identification of key nodes, we discovered that as compared with other centrality measures, Eigenvector and Eccentricity Centralities were better able to identify important nodes.

The centrality of vertices has been the key issue in social network analysis. Many centrality measures have been presented, such as degree, closeness, between's and eigenvector centrality. But eigenvector centrality is more suited than other centrality measures for finding prominent or key author in research professionals' relationship network. In this paper, we discuss eigenvector centrality and its application based on Network x. In eigenvector centrality first set every node a starting amount of influence then performs power iteration method. In network x the starting amount of influence of each node is 1/len(G). Therefore, we modify the eigenvector centrality algorithm and set the starting amount of influence of each node is the degree centrality of that node because eigenvector centrality is the extension of degree centrality and also implements the eigenvector centrality in weighted network.

Measurements of node centrality are based on characterizing the network topology structure in a certain perspective. Changing the network topology structure would affect the accuracy of the measurements. In this paper, we employ the Holme-Kim model to construct scale-free networks with tunable clustering, and consider the four measurements of classical centrality, including degree centrality, closeness centrality, betweenness centrality and the eigenvector centrality. For comparing the accuracy of the four centrality measurements, we simulate the susceptible-infected-recovered (SIR) spreading of the tunable clustering scale free networks. Experimental results show that the degree centrality and the betweenness centrality are more accurate in networks with lower clustering, while the eigenvector centrality performs well in high clustering networks, and the accuracy of the closeness centrality keeps stable in networks with variable clustering. In addition, the accuracy of the degree centrality and the betweenness centrality are more reliable in the spreading process at the high infectious rates than that of the eigenvector centrality and the closeness centrality. Furthermore, we also use the reconnected autonomous system networks to validate the performance of the four classical centrality measurements with varying cluster. Results show that the accuracy of the degree centrality declines slowly when the clustering of real reconnected networks increases from 0.3 to 0.6, and the accuracy of the closeness centrality has a tiny fluctuation when the clustering of real reconnected networks varies. The betweenness centrality is more accurate in networks with lower clustering, while the eigenvector centrality performs well in high clustering networks, which is the same as in the tunable clustering scale free networks. According to the spreading experiments in the artificial and real networks, we conclude that the network clustering structure affects the accuracy of the node centrality, and suggest that when evaluating the node influence, we can choose the degree centrality in the low clustering networks, while the eigenvector centrality and the closeness centrality are still in the high clustering networks. When considering the spreading dynamics, the accuracy of the eigenvector centrality and the closeness centrality is high, but the accuracy of the degree centrality and the betweenness centrality is more reliable in the spreading process at high infectious rates. This work would be helpful for deeply understanding of the node centrality measurements in complex networks.

Weighted brain networks in disease: centrality and entropy in human immunodeficiency virus and aging

Anomalies in network traffic are often detected using machine learning techniques, such a Artificial Neural Networks, Self-Organizing Maps, k-Nearest Neighbors, or Principal Component Analysis. These techniques are built upon certain predetermined features that are believed to be useful in detecting anomalies. Many researchers are using graph-based features, such as betweenness centrality or eigenvector centrality. The choice of these particular features is due to the assumption that they can be used to accurately predict an anomaly in the flow of traffic. However, there appears to be no solid foundation for these assumptions. This work investigates edge centralities and how accurately they predict anomalies using netflow data. We propose to use known traits of different network interactions to identify how information will flow. We will then predict which measures of centrality should be most applicable to these particular flows. Finally, using public cybersecurity data sets, we will investigate which measures of edge centrality accurately identify anomalies as outliers then make comparisons with our predictions. Ideally, this will allow us to choose graph-based features that are highly efficient in anomaly detection.

Recent developments in network theory have allowed for the study of the structure and function of the human brain in terms of a network of interconnected components. Among the many nodes that form a network, some play a crucial role and are said to be central within the network structure. Central nodes may be identified via centrality metrics, with degree, betweenness, and eigenvector centrality being three of the most popular measures. Degree identifies the most connected nodes, whereas betweenness centrality identifies those located on the most traveled paths. Eigenvector centrality considers nodes connected to other high degree nodes as highly central. In the work presented here, we propose a new centrality metric called leverage centrality that considers the extent of connectivity of a node relative to the connectivity of its neighbors. The leverage centrality of a node in a network is determined by the extent to which its immediate neighbors rely on that node for information. Although similar in concept, there are essential differences between eigenvector and leverage centrality that are discussed in this manuscript. Degree, betweenness, eigenvector, and leverage centrality were compared using functional brain networks generated from healthy volunteers. Functional cartography was also used to identify neighborhood hubs (nodes with high degree within a network neighborhood). Provincial hubs provide structure within the local community, and connector hubs mediate connections between multiple communities. Leverage proved to yield information that was not captured by degree, betweenness, or eigenvector centrality and was more accurate at identifying neighborhood hubs. We propose that this metric may be able to identify critical nodes that are highly influential within the network.

PurposeIn recent years, centrality measures have been extensively used to analyze real-world complex networks. Water distribution networks (WDNs), as a good example of complex networks, exhibit properties not shared by other networks. This raises concerns about the effectiveness of applying the classical centrality measures to these networks. The purpose of this paper is to generate a new centrality measure in order to stick more closely to WDNs features.Design/methodology/approachThis work refines the traditional betweenness centrality by adding a hydraulic-based weighting factor in order to improve its fit with the WDNs features. Rather than an exclusive focus on the network topology, as does the betweenness centrality, the new centrality measure reflects the importance of each node by taking into account its topological location, its demand value and the demand distribution of other nodes in the network.FindingsComparative analysis proves that the new centrality measure yields information that cannot be captured by closeness, betweenness and eigenvector centrality and is more accurate at ranking the importance of the nodes in WDNs.Practical implicationsThe following practical implications emerge from the centrality analysis proposed in this work. First, the maintenance strategy driven by the new centrality analysis enables practitioners to prioritize the components in the network based on the priority ranking attributed to each node. This allows for least cost decisions to be made for implementing the preventive maintenance strategies. Second, the output of the centrality analysis proposed herein assists water utilities in identifying the effects of components failure on the network performance, which in turn can support the design and deployment of an effective risk management strategy.Originality/valueThe new centrality measure, proposed herein, is distinct from the conventional centrality measures. In contrast to the classical centrality metrics in which the importance of components is assessed based on a pure topological viewpoint, the proposed centrality measure integrates both topological and hydraulic attributes of WDNs and therefore is more accurate at ranking the importance of the nodes.

BackgroundIdentification of essential proteins is always a challenging task since it requires experimental approaches that are time-consuming and laborious. With the advances in high throughput technologies, a large number of protein-protein interactions are available, which have produced unprecedented opportunities for detecting proteins' essentialities from the network level. There have been a series of computational approaches proposed for predicting essential proteins based on network topologies. However, the network topology-based centrality measures are very sensitive to the robustness of network. Therefore, a new robust essential protein discovery method would be of great value.ResultsIn this paper, we propose a new centrality measure, named PeC, based on the integration of protein-protein interaction and gene expression data. The performance of PeC is validated based on the protein-protein interaction network of Saccharomyces cerevisiae. The experimental results show that the predicted precision of PeC clearly exceeds that of the other fifteen previously proposed centrality measures: Degree Centrality (DC), Betweenness Centrality (BC), Closeness Centrality (CC), Subgraph Centrality (SC), Eigenvector Centrality (EC), Information Centrality (IC), Bottle Neck (BN), Density of Maximum Neighborhood Component (DMNC), Local Average Connectivity-based method (LAC), Sum of ECC (SoECC), Range-Limited Centrality (RL), L-index (LI), Leader Rank (LR), Normalized α-Centrality (NC), and Moduland-Centrality (MC). Especially, the improvement of PeC over the classic centrality measures (BC, CC, SC, EC, and BN) is more than 50% when predicting no more than 500 proteins.ConclusionsWe demonstrate that the integration of protein-protein interaction network and gene expression data can help improve the precision of predicting essential proteins. The new centrality measure, PeC, is an effective essential protein discovery method.