![]() More detailed information about these four centrality metrics and the procedures to individually compute them is available in. While DEG and EVC could be categorized as neighborhood-based centrality metrics, BWC and CLC could be categorized as shortest path-based centrality metrics. There exist several centrality metrics, each proposed to capture a particular topological aspect the four commonly studied centrality metrics are degree centrality (DEG), eigenvector centrality (EVC), betweenness centrality (BWC), and closeness centrality (CLC). Centrality metrics quantify the topological importance of the nodes in a network. vertices) in a complex network are either topology-based or domain-based or a combination of both. We evaluate the NSI values for a suite of 60 real-world networks with respect to both neighborhood-based centrality metrics (degree centrality and eigenvector centrality) and shortest path-based centrality metrics (betweenness centrality and closeness centrality). We refer to “1 − (minimum threshold distance )” as the node similarity index (NSI ranging from 0 to 1) for the complex network with respect to the k node-level metrics considered. We run a binary search algorithm to determine the minimum value for the threshold distance that would yield a connected unit disk graph of the vertices. There exists an edge between two vertices in the unit disk graph if the Euclidean distance between the two vertices in the normalized coordinate system is within a threshold value (ranging from 0 to, where k is the number of node-level metrics considered). In this pursuit, we propose the following unit disk graph-based approach: we first normalize the values for the node-level metrics (using the sum of the squares approach) and construct a unit disk graph of the network in a coordinate system based on the normalized values of the node-level metrics. They can communicate only if they are within mutual transmission range.We seek to quantify the extent of similarity among nodes in a complex network with respect to two or more node-level metrics (like centrality metrics). Nodes are located in the Euclidean plane and are assumed to have identical (unit) transmission radii. One prominent application of unit disk graphs can be found in the eld of wireless networking, where a unit disk graph represents an idealized multi-hop radio network. Unit disk graphs have proven to be useful in modeling various physical real world problems. Equivalently, each node is identi ed with a disk of unit radius r = 1 in the plane, and is connected to all nodes within (or on the edge of) its corresponding disk. INTRODUCTION In a unit disk graph, there is an edge between two nodes u and v if and only if the Euclidean distance between u and v is at most 1. Unit Disk Graph Approximation Fabian Kuhn Computer Engineering and Networks Laboratory ETH Zurich 8092 Zurich, Switzerland Thomas Moscibroda Computer Engineering and Networks Laboratory ETH Zurich 8092 Zurich, Switzerland Roger Wattenhofer Computer Engineering and Networks Laboratory ETH Zurich 8092 Zurich, Switzerland ABSTRACT 1. Clearly, the unit disk graph model neatly captures this behavior and it is not surprising that it has They can communicate only if they are within mutual transmission range. Kuhn, Fabian Moscibroda, Thomas Wattenhofer, Roger Unit disk graph approximation Unit disk graph approximation ![]()
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