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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
Consequently, the graph has a group clustering coefficient of C = k/N where k is the mean degree, and the statistical distribution of the degrees for all possible realizations of the Erdös–Rényi networks follows the Poisson probability distribution as the number of nodes grows large. One downside to the Erdös–Rényi graph generating algorithm is that it is not scale-free (Barabási & Albert, 1999), a property possessed by many real-world social networks such as the World Wide Web (Albert, Jeong & Barabási, 1999). A scale-free network is defined as one that has a power law degree distribution between nodes, which typically means that many nodes have few connections and only a smaller proportion of nodes have many connections. The Erdös–Rényi generated graph contains nodes that are randomly connected. However, given its history, the Erdös–Rényi algorithm is widely used as a baseline for comparisons of network metrics and classification.
Complex Systems
Published in Pier Luigi Gentili, Untangling Complex Systems, 2018
The node that has the largest degree increases further its connectivity and becomes a hub. “The rich get richer.” Scale-free networks have two key features: robustness to random failure and vulnerability to hubs’ attack (Albert et al. 2000). The robustness of the scale-free networks is rooted in their inhomogeneous connectivity. In fact, the power-law distribution guarantees that the majority of nodes have only a few links and that there are just a few hubs. The probability that random failure involves nodes with low connectivity is much higher. Therefore, the failure of nodes scarcely connected does not affect the overall topology and the average length of the shortest paths. However, the removal of a few key hubs splinters the network into small isolated clusters of nodes.
Complex Network Theory
Published in Andrew Cook, Damián Rivas, Complexity Science in Air Traffic Management, 2016
Andrew Cook, Massimiliano Zanin
So what do all these findings tell us? They suggest that the Internet has a scale-free structure, in which large hubs control large groups of small nodes, organised both according to a hierarchical and spatially constrained structure. Far from being a purely theoretical classification, understanding the class to which a real-world network belongs furnishes valuable insights with regard to optimisation and vulnerability. For example, it is well established that scale-free networks are highly resilient to random failures, as most of the nodes have a low number of connections, and therefore their removal would not dramatically affect the whole network dynamics. Nevertheless, this does come at a high price, since they are particularly vulnerable to targeted attacks (Albert et al., 2000). Specifically, a smart attack can target an important hub, disrupting the behaviour of the dependent nodes, thus affecting the functioning of the Internet in a particular geographical region. Notably, small-world and random networks behave in opposite ways. Consider a random network. In this case, an attacker could not identify a highly important node, and therefore these types of network are resilient to targeted attacks. On the other hand, since no nodes are really secondary, such an attack may be expected to cause significant damage. Deploying CNT towards an improved understanding and characterisation of such network topologies, and the identification of, for example, the underlying network class and most central nodes, often affords powerful insights into identifying critical elements of such systems.
Structure, characteristics and connectivity analysis of the Asian-Australasian cruise shipping network
Published in Maritime Policy & Management, 2022
Maneerat Kanrak, Hong-Oanh Nguyen
The Barabási-Albert model features random scale-free networks with two mechanisms: (i) they grow in terms of the number of nodes and (ii) new links are formed preferentially (preferential attachment) as a new node attached preferentially to those that are already well connected. The latter property implies that ‘the rich get richer’. It models scale-free networks that have shorter average path lengths and larger clustering coefficients than random graphs of the same size. Scale-free networks can be regarded as ultra-small worlds, as shown by Cohen, Havlin, and Ben-Avraham (2003) and Cohen and Havlin (2003). Many real-world networks have thought to be scale-free networks that contain few nodes with large degrees (hubs) and a majority of nodes with small degrees (Beauguitte and Ducruet 2011). In the transport network, Sapre (2011) found that the air transport network in India had a smaller average path length, but a larger clustering coefficient than an equivalent random network.
Research on supply network resilience considering random and targeted disruptions simultaneously
Published in International Journal of Production Research, 2020
Xiao-qiu Shi, Wei Long, Yan-yan Li, Ding-shan Deng, Yong-lai Wei, Hua-guo Liu
Figure 5 illustrates the responses of the five models to targeted disruptions. As shown in Figure 5(a), almost 46% of the BA models begin to be completely destroyed when 120 nodes are removed, and more than 50% of the networks are completely destroyed when 140 nodes are removed. This means that the scale-free network is very vulnerable to targeted disruptions. On the contrary, almost 28% of the ER models begin to be completely destroyed when 180 nodes are removed, which means that the performance of the ER model against targeted disruptions is better than that of the BA model. Figure 5(a) also shows that the ER model performs best. Slightly behind the ER model, almost 3% of the GMD-G models are completely destroyed when 160 nodes are removed, which means that the performance of the GMD-G model against targeted disruptions is similar to that of the ER model. Figure 5(b and c) depict the decreasing performance order of the models as ER, GMD-G, GMD-M, GMD-D, and BA. These results indicate that the BA model is very vulnerable to targeted disruptions but very resilient to random disruptions; the ER model is very resilient to both random and targeted disruptions; and, slightly behind ER, the GMD-G model performs well against both disruptions.
A cyber-physical system architecture based on lean principles for managing industry 4.0 setups
Published in International Journal of Computer Integrated Manufacturing, 2022
Amr Nounou, Hadi Jaber, Ridvan Aydin
Scale-free networks are a type of network characterized by the presence of large hubs. A scale-free network is one with a power-law degree distribution. A scale-free network can be constructed by progressively adding nodes to an existing network and introducing links to existing nodes with preferential attachment. So that the probability of linking to a given node i is proportional to the number of existing links ki that node i has. “ Consequently, this link distribution leads to obtaining hubs of a very high degree.