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Modern Methods for Characterization of Social Networks through Network Models
Published in Natalie M. Scala, James P. Howard, Handbook of Military and Defense Operations Research, 2020
Christine M. Schubert Kabban, Fairul Mohd-Zaid, Richard F. Deckro
Erdös and Rényi proposed the first commonly used random graph generating model (1959) in which a graph is generated by connecting any pair of nodes with an edge with probability p, and in which each edge is independent from every other edge. This results in a graph of N nodes and m edges having an equal probability of pm1−pN2−m
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].
Sensor Network Security
Published in Vidushi Sharma, Anuradha Pughat, Energy-Efficient Wireless Sensor Networks, 2017
Aarti Gautam Dinker, Vidushi Sharma
The above-discussed schemes have few limitations for large or dynamic WSNs, the reason being that the storage of too many keys, joining and leaving, or rekeying of sensor nodes are complex and expensive in terms of resources. These disadvantages were addressed in the probabilistic key predistribution scheme (Eschenauer and Gligor 2002). In this scheme, communication keys are established in three phases: key predistribution, shared-key discovery, and path-key establishment. For key predistribution, a large pool of P keys is generated and then k distinct keys out of P are drowned and loaded into each sensor node memory. The security of a communication depends upon the key connectivity for discovering the shared key and establishing the path key. Connectivity of the WSN can be analyzed and studied from the random graph theory (Spencer 2000). A graph of n nodes, in which the probability that a connection can be established between two nodes is p, can be called as a random graph. The link can be the shared key in the WSN. This scheme provides good authentication and scalability, but resiliency to sensor node capture is still a concern.
Centrality and connectivity analysis of the European airports: a weighted complex network approach
Published in Transportation Planning and Technology, 2023
A random graph is defined as a graph with a random distribution of edges. A random graph with N vertices, each having a connection probability p, the degrees of vertices are distributed to obey the binomial distribution: This is the probability of a certain vertex to have k edges of which the endpoints can be chosen in different ways. In this research paper, we use Erdös-Renyi random graph model to simulate a random network (Albert and Barabasi 2002).
A topological characterisation of looped drainage networks
Published in Structure and Infrastructure Engineering, 2022
Didrik Meijer, Hans Korving, François Clemens-Meyer
Until the 1950s, complex networks were mainly studied as regular graphs using graph theory. Since the 1950s, complex networks have been described as random graphs. A widely used model for studying random graphs is the Erdós-Rényi model. This model starts with N nodes and every edge is formed with probability p independently of every other edge. This results in a graph with approximately edges distributed randomly (Albert & Barabási, 2002).
Small-world architecture of networked control systems
Published in International Journal of Control, 2018
Network Science as summarised by Albert and Barabási (2002), Lewis (2009), Newman (2010) or Watts and Strogatz (1998) has shown that large real-world graphs have the small-world property. That is, any pair of vertices is connected by a path of small length. More formally, the mean length of paths between all vertex pairs in a random graph does not grow faster than log N, where N is the number of vertices (Erdös & Rényi, 1959).