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Definition, classification, and methodological issues of system of systems
Published in Mo Jamshidi, Systems of Systems Engineering, 2017
Marcus Bjelkemyr, Daniel T. Semere, Bengt Lindberg
Both small-world and scale-free networks are the result of three statistical network characteristics that are derived using graph theory: average path length, clustering coefficient, and degree distribution. Average path length is defined as the average least number of steps between any two nodes in a network, and it is a measure of the efficiency of a network. With a shorter average path length, fewer steps are on average required to distribute information or mass inside the network. The clustering coefficient is defined as the probability that two nodes, which both are connected to a third node, also are connected to each other. Consequently, the clustering coefficient is a measure of the network’s potential modularity [11]. The third characteristic, degree distribution, is the distribution of the number of edges for all the nodes in a network.
Social Networks
Published in Vivek Kale, Agile Network Businesses, 2017
Network efficiency can be measured by considering the number of nodes that can instantly access a large number of different nodes—sources of knowledge, status, and so on—through a relatively small number of ties. These nodes are treated as nonredundant contacts. For example, with two networks of equal size, the one with more nonredundant contacts provides more benefits than the others. Also, it is quite evident that the gain from a new contact redundant with existing contacts will be minimal. However, it is wise to consume time and energy in cultivating a new contact to unreached people. Hence, social network analysts measure efficiency by the number of nonredundant contacts and the average number of ties an ego has to traverse to reach any alter; this number is referred to as the average path length. The shorter the average path length relative to the size of the network and the lower the number of redundant contacts, the more efficient is the network.
Beyond NEC
Published in Guy H. Walker, Neville A. Stanton, Paul M. Salmon, Daniel P. Jenkins, Command and Control: The Sociotechnical Perspective, 2009
Guy H. Walker, Neville A. Stanton, Paul M. Salmon, Daniel P. Jenkins
Distributed Networks: in appearance, this architecture looks a little like a city street plan organised along grid principles, with each junction representing a crossroads. A distinct property of this network architecture is that as the network grows, so does the average path length between one node and another. In this case words, the number of steps to get from one point in the network increases more or less linearly with the network’s size. Given that the internet, for example, is forecast to grow in size by 1000 per cent in the next few years, this sort of growth would be accompanied by a more or less 1000 per cent increase in the distance (and number of intermediate servers/computers) that would be required to reach a desired web page, accompanied by a corresponding increase in time to negotiate such a complex route (Ball, 2004).
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).
Structure, characteristics and connectivity analysis of the Asian-Australasian cruise shipping network
Published in Maritime Policy & Management, 2022
Maneerat Kanrak, Hong-Oanh Nguyen
The small-world network model proposed by Watts and Strogatz (1998), refers to networks with a large clustering coefficient and a smaller average path length than the ER networks. Moreover, the average shortest length (l) grows proportionately with the natural log of the number of nodes (n): . It reflects networks comprising of small clients, clusters, or cliques with connections between almost any two nodes within them. A small-world network has a small average path length, and this is typical because nodes are connected to others through hubs that form clusters. This means a small-world network tends to have a high cluster coefficient. In Soh et al. (2010)’s study, the rapid transit system and bus networks were found to have the larger clustering coefficients and smaller average path lengths than random graphs with the same number of nodes and links. The degree distributions of these networks followed a power law, indicating that they were characterised by a small-world property. Couto et al. (2015) revealed that the Brazilian air transport network also exhibited a small-world characteristic with the degree distribution followed a power law.
A streamlined approach for evaluating post-earthquake performance of an electric network
Published in Sustainable and Resilient Infrastructure, 2020
Amir Sarreshtehdari, Negar Elhami Khorasani, Maxwell Coar
This section applies the proposed methodology to evaluate performance of the two electric networks in Los Angeles (L.A.), after the 1994 Northridge earthquake and Shelby County in the New Madrid seismic zone. Table 4 compares the topological characteristics of the two electric networks. The Shelby County network has larger number of nodes and edges, while the L.A. network is a more efficient and connected network. The average path length represents the average number of edges that need to be crossed to move from one node to another in the network. A shorter path length is more desirable, facilitating faster transfer of power, and implies less loss in a power grid. The average clustering coefficient calculates the number of neighboring nodes that are connected together. A larger value for clustering coefficients implies more connected nodes. The L.A. power network has a smaller average path length with a larger average clustering coefficient and is better structured compared to the Shelby County network. Table 4 compares the characteristics of the two networks.