The Fractional Preferential Attachment Scale-Free Network Model

Abstract

Many networks generated by nature have two generic properties: they are formed in the process of preferential attachment and they are scale-free. Considering these features, by interfering with mechanism of the preferential attachment, we propose a generalisation of the Barabási–Albert model—the ’Fractional Preferential Attachment’ (FPA) scale-free network model—that generates networks with time-independent degree distributions p ( k ) ∼ k − γ with degree exponent 2 < γ ≤ 3 (where γ = 3 corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the f parameter, where f ∈ ( 0 , 1 ⟩ . Depending on the different values of f parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on f, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that f parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of f, FPA networks are not fractal.

A Novel Method to Rank Influential Nodes in Complex Networks Based on Tsallis Entropy

“…In this paper, six random synthetic Barabasi Albert (BA) scale-free networks [ 28 ] of different sizes, four random synthetic Fractional Preferential Attachment (FPA) scale-free networks [ 29 ] of different ‘f’ parameter, and 10 real networks of different sizes are selected. Table 1 shows the analysis data of 10 random synthetic scale-free networks, and Table 2 shows the analysis data of 10 real networks, including the number of nodes, the number of edges, the average degree, the maximum degree, the assortativity, and the clustering coefficient.…”

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“…We first find the exact value of constant C from Equation (16). Let P(i, j) denote the probability that vertex v i is connected to the vertex v j at the moment of its appearance at time i, i.e., P(i, j) =…”

“…Using the mechanisms of growth and preferential attachment, the model made it possible to describe the evolution of networks with the power-law degree distribution. In recent years, researchers have proposed many extensions of this model, to approximate the properties of real systems [10][11][12][13][14][15][16][17][18][19][20]. Nevertheless, studying the peculiarities of networks generated by the pioneering Barabási-Albert model is of interest, as it sheds light on the properties of extended models [21].…”

A modified gravity model based on network efficiency for vital nodes identification in complex networks

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