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Network science
Published in Benjamin S. Baumer, Daniel T. Kaplan, Nicholas J. Horton, Modern Data Science with R, 2021
Benjamin S. Baumer, Daniel T. Kaplan, Nicholas J. Horton
In particular, many real-world networks, including not only social networks but also the World Wide Web, citation networks, and many others, have a degree distribution that follows a power-law. These are known as scale-free networks and were popularized by Albert-László Barabási in two widely-cited papers (Barabási and Albert, 1999, (Albert and Barabási, 2002)] and his readable book (Barabási and Frangos, 2014). Barabási and Albert proposed a third random graph model based on the notion of preferential attachment. Here, new nodes are connected to old nodes based on the existing degree distribution of the old nodes. Their model produces the power-law degree distribution that has been observed in many different real-world networks.
Networks: The Basics
Published in Ian Foster, Rayid Ghani, Ron S. Jarmin, Frauke Kreuter, Julia Lane, Big Data and Social Science, 2020
Most importantly, the degree distribution is commonly taken to provide insight into the dynamics by which a network was created. Highly skewed degree distributions often represent scale-free networks (Barabási and Albert, 1999; Newman, 2005; Powell et al., 2005), which grow in part through a process called preferential attachment, where new nodes entering the network are more likely to attach to already prominent participants. In the kinds of scientific collaboration networks that UMETRICS represents, a scale-free degree distribution might arise as faculty new to an institution attempt to enroll more established colleagues on grants as coinvestigators. In the comparison exercise outlined next, I plot degree distributions for the main components of two different university networks.
Literature review and proposed framework
Published in Juan Carlos Chacon-Hurtado, Optimisation of Dynamic Heterogeneous Rainfall Sensor Networks in the Context of Citizen Observatories, 2019
Recently, research efforts have been devoted to the use of the so-called network theory to assess the performance of discharge sensor networks (Halverson and Fleming 2015, Sivakumar and Woldemeskel 2014). These studies analyse three main features, namely average clustering coefficient, average path length and degree distribution. Average clustering is a degree of the tendency of stations to form clusters. Average path length is the average of the shortest paths between every combination of station pairs. Degree distribution is the probability distribution of network degrees across all the stations, being network degree defined as the number of stations to which a station is connected. Halverson and Fleming (2015) observed that regular streamflow networks are highly clustered (so the removal of any randomly chosen node has little impact on the network performance) and have long average path lengths (so information may not easily be propagated across the network).
A topological characterisation of looped drainage networks
Published in Structure and Infrastructure Engineering, 2022
Didrik Meijer, Hans Korving, François Clemens-Meyer
Albert and Barabási (2002) also observe that since the 1990s, three concepts play an important role in network analyses:The small-world concept: there is a relatively short path between any two nodes, even in large networks. The path length is defined as the number of edges along the shortest path (Watts, 1999; Watts & Strogatz, 1998).Clustering: cliques are common in social networks. In these circles of acquaintances, every member knows every other member. The degree of clustering can be expressed with the clustering coefficient: where ki is the number of edges connected to node i and Ei is the total number of edges.Scale-free networks and degree distribution (degree is the number of edges that are connected to the node): the distribution of the node degree P(k) for large networks has a power-law tail as follows: where P(k) is the distribution of the node degree and k is the node degree.
Structure, characteristics and connectivity analysis of the Asian-Australasian cruise shipping network
Published in Maritime Policy & Management, 2022
Maneerat Kanrak, Hong-Oanh Nguyen
The above statistical measures and models are applied to the cruise shipping network. Network density is used to analyse the network’s connectivity level, while degree distribution is used to identify the network characteristics and global connectivity. Degree centrality identifies hub ports and their connectivity levels. Betweenness centrality is used to determine port accessibility and central ports that play an intermediate role in the network. Closeness centrality is used to analyse reachability and accessibility. The measure of eigenvector centrality is used to identify ports’ role in the network, especially connections to central ports. Therefore, it is useful for studying the development potential and competitiveness of ports. The statistics of the actual network are also compared with those of equivalent random networks with the same number of nodes and links. ERGMs are then applied to study the formation of the network links. The methodology flow chart of this study is presented in Figure 1.
Vulnerability analysis of inland waterways network base on complex network theory
Published in International Journal of Computers and Applications, 2020
Huang Changhai, Hu Shenping, Kong Fancun, Xuan Shaoyong
The degree of a node i is defined as the number of other nodes connected to this node. The degree of a node in a directed network is divided into out-degree and in-degree. The out-degree of a node refers to the number of edges pointing from the node to other nodes; the in-degree of the node refers to the number of edges pointing from other nodes to this node. The average value of the degree of all nodes i in the network is called the average degree of the network (nodes), denoted by . The degree distribution of nodes in the network can be described by the distribution function P(k). P(k) refers to the probability that a randomly selected node has exactly the degree k.