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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
The clustering coefficient is a measure of how much the nodes cluster together. High clustering indicates that nodes are highly interconnected. The clustering coefficient (CC) for a given station is defined as: CC(α)=2k(α)(k(α)−1)∑j=1naα,j
A New Approach for Groundwater Modeling Based on Connections
Published in M. Thangarajan, Vijay P. Singh, Groundwater Assessment, Modeling, and Management, 2016
B. Sivakumar, X. Han, F. M. Woldemeskel
Encouraged by the outcomes of the above studies, we make an attempt here to apply, for the first time, the concepts of complex networks in the field of groundwater hydrology. Specifically we examine the spatial connections in a groundwater level monitoring network in a region. For this purpose, daily groundwater levels observed across 125 wells in California are analyzed using two complex networks-based methods: clustering coefficient and degree distribution. The clustering coefficient is a measure of local density and quantifies the tendency of a network to cluster. The degree distribution is a measure of spread and expresses the fraction of nodes in a network with a certain number of links. The results are interpreted to obtain important information about the type of the groundwater level monitoring network.
Similarity Principle—The Fundamental Principle of All Sciences
Published in Mark Chang, Artificial Intelligence for Drug Development, Precision Medicine, and Healthcare, 2020
where ki is the number of neighbors (nodes) of the ith node, and ei is the number of connections between these neighbors. ki (ki − 1)/2 is the maximum possible number of connections between neighbors. The clustering coefficient for the entire network is the average of the clustering coefficients of all the nodes. A high clustering coefficient for a network is another indication of a small world. See Chapter 10 for more information.
Open big data from ticketing website as a useful tool for characterizing spatial features of the Chinese high-speed rail system
Published in Journal of Spatial Science, 2018
Sheng Wei, Jiangang Xu, Jingwei Sun, Xuejiao Yang, Ran Xin, Da Shen, Kai Lu, Maosong Liu, Chi Xu
The clustering coefficient is used to quantify the extent to which nodes connected to the same node in the network are also neighbours to each other (i.e. the ‘small-world’ property). The average clustering coefficient of the network describes the probability of connecting to each other among any three nodes, and reflects the close relationship of these nodes in the whole network. The procedure for calculating the clustering coefficient is as follows. Assuming that the node i is connected to other ki nodes through ki edges and these ki nodes are also connected to each other. Therefore, the maximum number of edges among these ki nodes should be ki(ki −1)/2. However, the actual number of edges among these ki nodes is Ei, then the clustering coefficient of the node i is the ratio of Ei and ki(ki −1)/2. The clustering coefficient is expressed as Equation (3).
The properties of global risk networks and corresponding risk management strategies
Published in Human and Ecological Risk Assessment: An International Journal, 2018
Upon developing the global risk network, we analyze a few important network properties to determine the hub nodes and topological structure of the network. Node degrees, average path length, and clustering coefficients are the three most important network properties. Node degree is the number of edges connected to a particular node and has important implications for which nodes are most detrimental to the cascading failures and system stability. Average path length is a measure of the efficiency of mass transport on a network and can show how the network is scattered. The distance duv between two nodes u and v is defined as the number of links along the shortest path connection, If n nodes exist in the network, then the average path length L of the network can be defined as . The clustering coefficient is a measure of the degree to which the nodes in a network tend to cluster together. In network theory, the tendency of link formation between neighboring nodes in a network is called clustering or transitivity. The clustering coefficient is also a local property that determines “the density” of triangles in the graph. If a node vi has ki neighbors, then edges could exist among the nodes within the neighborhood. Thus, the clustering coefficient of the node vi can be defined as and is the precise number of edges among the neighborhood of the node vi.
Exploring public bicycle network structure based on complex network theory and shortest path analysis: the public bicycle system in Yixing, China
Published in Transportation Planning and Technology, 2019
Sheng Wei, Jiangang Xu, Haitao Ma
The clustering coefficient is used to describe the extent to which nodes connected to the same node in the network are also neighbors. The average clustering coefficient of the network describes the probability of connecting each other among any three nodes, and reflects the close relationship of these nodes in the whole network.