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Power Grid Network Analysis for Smart Grid Applications
Published in David Bakken, Krzysztof Iniewski, Smart Grids, 2017
Zhifang Wang, Anna Scaglione, Robert J. Thomas
Power grids have been found to have the salient features of small-world graphs (see the work by Watts and Strogatz [1]). That is, while the vast majority of links are similar to those of a regular lattice, with limited near-neighbor connectivity, a few links connect across the network. These bridging links significantly shorten the path length that connects every two nodes and critically increase the connectivity of the network. At the same time, their scarcity puts the connectivity at risk in the case of link failure for one of these critical bridges. The characterizing measure to distinguish a small-world network is called the clustering coefficient, which assesses the degree to which nodes tend to cluster together. A small-world network usually has a clustering coefficient significantly higher than that of a random graph network, given the comparable network size and total number of edges. The random graph network mentioned here refers to the network model defined by Erdös and Rényi, with n labeled nodes connected by m edges that are chosen uniformly randomly from the n(n − 1)/2 possible edges [10].
An analysis of open source operating systems based on complex networks theory
Published in Jimmy C.M. Kao, Wen-Pei Sung, Civil, Architecture and Environmental Engineering, 2017
Denghui Zhang, Zhengxu Zhao, Yiqi Zhou, Yang Guo
In a random network, there is C¯~1/n. However, it has been shown that nodes have a strong tendency to form groups, which means real networks has a bigger clustering coefficient compared to random networks. Especially, a network with highly clustering coefficient like regular networks and small average path length like random network is called small world networks.
Some Mathematical Properties of Networks for Big Data
Published in Yulei Wu, Fei Hu, Geyong Min, Albert Y. Zomaya, Big Data and Computational Intelligence in Networking, 2017
Small-world networks were first investigated as a class of random graphs, which tend to have a small average shortest path length, and a small clustering coefficient. However, small-world networks were soon grouped into a different type of network due to a higher clustering coefficient, compared to random networks. This motivated the introduction of the Watts and Strogatz model, which has proved successful in modeling a variety of real-world scenarios [9].
Centrality and connectivity analysis of the European airports: a weighted complex network approach
Published in Transportation Planning and Technology, 2023
A small-world network can be defined as a network in which there are many vertices, but the average path length of the network is relatively small. This characteristic is thought to be inherent in most real-world networks. Another characteristic of small-world networks is their relatively large clustering coefficients which is also known to be independent of network size. We use the Watts-Strogatz model to simulate a small-world network in this study (Watts and Strogatz 1998). The degree distribution of such networks is similar to that of random graphs, where each vertex has approximately the same number of edges. An example to a social small-world network is the concept that all people are six or fewer connections away from each other or the so-called ‘six degrees of separation’ (Guare 2016).
A review of research in illicit supply-chain networks and new directions to thwart them
Published in IISE Transactions, 2021
Rashid Anzoom, Rakesh Nagi, Chrysafis Vogiatzis
Based on their structure, one may classify networks as random Erdős-Rényi (ER) (Erdős and Rényi, 1959), small-world (Watts and Strogatz, 1998), or scale-free (Barabási and Albert, 1999). Random ER networks possess links with the same probability of existence. Small-world networks are associated with high clustering and small characteristic path length (diameter). Although in these networks most nodes are not adjacent, they tend to share neighbors. In a similar vein, most nodes in scale-free networks also follow this characteristic. A small number of nodes, referred to as hubs, show high connectivity. This property is consistent with the power-law degree distribution.
Stochastic pretopology as a tool for complex networks analysis
Published in Journal of Information and Telecommunication, 2019
Quang Vu Bui, Soufian Ben Amor, Marc Bui
Complex system is a system composed of many interacting parts, such that the collective behaviour of its parts together is more than the ‘sum’ of their individual behaviours (Newman, 2011). The topology of complex systems (who interact with whom) is often specified in terms of complex networks that are usually modelled by graphs, composed by vertices or nodes and edges or links. Graph theory has been widely used in the conceptual framework of network models, such as random graphs, small world networks, scale-free networks (Easley & Kleinberg, 2010; Newman, 2003).