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Structure of networks
Published in Karthik Raman, An Introduction to Computational Systems Biology, 2021
Closeness centrality [6] tries to quantify the centrality of a node, based on its proximity to all other nodes in the network. The mean geodesic distance from a given node to all other nodes in a network is given as Li=1n−1∑j(≠i)dij
Message Forwarding Strategies
Published in Yufeng Wang, Athanasios V. Vasilakos, Qun Jin, Hongbo Zhu, Device-to-Device based Proximity Service, 2017
Yufeng Wang, Athanasios V. Vasilakos, Qun Jin, Hongbo Zhu
In graph theory and network analysis, centrality is a quantitative measure of the topological importance of a vertex within the graph. There are several ways to define centrality in a graph: degree centrality, betweenness centrality, and closeness centrality [8]. Degree centrality is the simplest centrality measure, which is defined as the number of links (i.e., direct contacts) incident on a given node. A node with a high-degree centrality is a popular node with a large number of possible contacts, and thus it is a good candidate of a message forwarder for others (i.e., a hub for information exchange among its neighborhood). Betweenness centrality measures the number of shortest paths passing via certain given node. Nodes that occur on many shortest paths between other nodes have higher betweenness than those that do not. A node with high betweenness centrality can control or facilitate many connections between other nodes, thus it is ideal for a bridge node during message exchange. The closeness centrality of a node is defined as the inverse of its average shortest distance to all other nodes in the graph. If a node is near to the centre of the graph, it has higher closeness centrality and is good for quickly spreading messages over the network.
Getting Social: Graph Theory and Social Network Analysis
Published in Jesús Rogel-Salazar, Advanced Data Science and Analytics with Python, 2020
There are cases where we may be interested in finding out which nodes are able to spread information more efficiently through the network. In those cases, the centrality measure we are interested in is called closeness. The closeness centrality of a node is proportional to the inverse of the average distance from the node to the rest of the network. In this way, a node with high closeness centrality has the shortest distances to all the other nodes. This can be expressed as follows: ()C(υ)=N∑xd(υ,x)′ where d(υ, x) is the distance between nodes υ and x, and N is the number of nodes in the graph. Closeness centrality is sensitive to the size of the graph. As you intuitively know, it is harder to keep a close relationship with every single one of the members in a network, and as the network grows in size this gets harder and harder. Multiplying by the number of nodes provides a form of correction for this situation. Closeness centrality tells us about the nodes that are able to spread information more efficiently in the network.Closeness centrality is sensitive to the size of the network.
VoteSumm: A Multi-Document Summarization Scheme Using Influential Nodes of Multilayer Weighted Sentence Network
Published in IETE Technical Review, 2023
Raksha Agarwal, Niladri Chatterjee
Closeness centrality indicates how close a node is to all other nodes in the network. It is calculated as the reciprocal of the average of the shortest path length from the node to every other node in the network [22]. If the network contains nodes and denotes the shortest path length between node and node then the Closeness centrality of node is calculated as given in Equation (6), where denotes the set of nodes that are reachable from node and is the cardinality of . Here, reachable means that the nodes are either connected through a single edge or a sequence of edges.
Resilience metrics and measurement methods for transportation infrastructure: the state of the art
Published in Sustainable and Resilient Infrastructure, 2020
Wenjuan Sun, Paolo Bocchini, Brian D. Davison
Distance-based centrality measures include closeness centrality (Cheng et al., 2015; Julliard et al., 2015) and betweenness centrality (Cheng et al., 2015; Jordan, 2008; Julliard et al., 2015; Leu et al., 2010; Rokneddin et al., 2013; Wang et al., 2015; Wang et al., 2008). The closeness centrality of a node is the inverse of the average shortest path distance from the node to any other node in the network. Betweenness centrality was originally proposed by Anthonisse (1971) and Freeman (1977), to describe to what extent a particular node lies between other nodes in the network. A node with a great betweenness centrality is on the shortest paths connecting many nodes. Therefore, it would be a critical node in the network that should be considered for pre-event strengthening interventions and given the top priority in post-event restoration to increase the resilience of the transportation network.
A comparison of centrality measures and their role in controlling the spread in epidemic networks
Published in International Journal of Control, 2023
Ekaterina Dudkina, Michelangelo Bin, Jane Breen, Emanuele Crisostomi, Pietro Ferraro, Steve Kirkland, Jakub Mareček, Roderick Murray-Smith, Thomas Parisini, Lewi Stone, Serife Yilmaz, Robert Shorten
As with degree centrality, the definition of closeness centrality can be extended to directed networks, though a distinction must be made on whether the distances are computed from, or to, the reference node i, respectively. Note also that ‘distances’ are not symmetric in directed networks. For weighted graphs, one could consider the edge-weights as a ‘cost’ to traversing the edge, and thus define shortest-distance between u and v as the minimum weight of any path from u to v (where the weight of a path is the sum of the weights of edges in the path). With such a definition for distance in hand, it is reasonable to generalise the closeness centrality for weighted graphs; see Opsahl et al. (2010) for some limited discussion.