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A scale-free network is a network whose degree distribution follows a power law, at least asymptotically.That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as
A scale-free network is a type of networks that is of particular interest of network science.It is characterized by its degree distribution following a power law. While the most widely known generative models for scale-free networks are stochastic, such as the Barabási–Albert model or the Fitness model can reproduce many properties of real-life networks by assuming preferential attachment ...
The Barabási–Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism. Several natural and human-made systems, including the Internet, the World Wide Web, citation networks, and some social networks are thought to be approximately scale-free and certainly contain few nodes (called hubs) with unusually high degree as compared to ...
Many real networks have two fundamental properties, scale-free property and small-world property. If the degree distribution of the network follows a power-law, the network is scale-free; if any two arbitrary nodes in a network can be connected in a very small number of steps, the network is said to be small-world.
An example of complex scale-free network. A network is called scale-free [6] [14] if its degree distribution, i.e., the probability that a node selected uniformly at random has a certain number of links (degree), follows a mathematical function called a power law. The power law implies that the degree distribution of these networks has no ...
The hierarchical network model is part of the scale-free model family sharing their main property of having proportionally more hubs among the nodes than by random generation; however, it significantly differs from the other similar models (Barabási–Albert, Watts–Strogatz) in the distribution of the nodes' clustering coefficients: as other models would predict a constant clustering ...
In network science, a hub is a node with a number of links that greatly exceeds the average. Emergence of hubs is a consequence of a scale-free property of networks. [1]: 27 While hubs cannot be observed in a random network, they are expected to emerge in scale-free networks.
For such scale-free networks the degree distribution approximately follows a power law: (), where γ is the degree exponent, and is a constant. Such scale-free networks have unexpected structural and dynamical properties, rooted in the diverging second moment of the degree distribution. [9] [10] [11] [12]