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Journal articles on the topic 'Preferential attachment'

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Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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1

Tameirão, Cinthya Rocha, Sérgio Fernando Loureiro Rezende, and Luciana Pereira de Assis. "Ligação Preferencial e Aptidão na Evolução da Rede de Filmes Brasileiros." Organizações & Sociedade 28, no. 99 (December 2021): 888–916. http://dx.doi.org/10.1590/1984-92302021v28n9907pt.

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Abstract This study analyzes the network evolution, specifically that of the Brazilian film network. It examines two generative mechanisms that lie behind the network evolution: preferential attachment and fitness. The starting point is that preferential attachment and fitness may compete to shape the network evolution. We built a novel dataset with 974 Brazilian feature films released between 1995 and 2017 and used PAFit, a brand-new statistical method, to estimate the joint effects of preferential attachment and fitness on the evolution of the Brazilian film network. This study concludes that the network evolution is shaped by both preferential attachment and fitness. However, in the presence of fitness, the effects of preferential attachment on the network evolution become weaker. This means that the node ability to form ties in the Brazilian film network is mainly explained by its fitness. Besides, the preferential attachment assumes a sub-linear form. Costs, communication and managerial capabilities, and node age explain why nodes are unable to accumulate ties at rates proportional to their degree. Finally, preferential attachment and fitness manifest themselves heterogeneously, depending on either the type or the duration of the network. Preferential attachment drives the cast network evolution, whereas fitness is the main generative mechanism of the crew network. Actors and actresses rely on their status, privilege, and power to obtain future contracts (preferential attachment), whereas technical members are selected on the basis of their talent, skills, and knowledge (fitness). Due to node age or exit, preferential attachment becomes stronger in shorter networks.

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2

Janson, Svante, Subhabrata Sen, and Joel Spencer. "Preferential attachment when stable." Advances in Applied Probability 51, no. 4 (November 15, 2019): 1067–108. http://dx.doi.org/10.1017/apr.2019.42.

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AbstractWe study an urn process with two urns, initialized with a ball each. Balls are added sequentially, the urn being chosen independently with probability proportional to the $\alpha$th power $(\alpha >1)$ of the existing number of balls. We study the (rare) event that the urn compositions are balanced after the addition of $2n-2$ new balls. We derive precise asymptotics of the probability of this event by embedding the process in continuous time. Quite surprisingly, fine control of this probability may be leveraged to derive a lower-tail large deviation principle (LDP) for $L = \sum_{i=1}^{n} ({S_i^2}/{i^2})$, where $\{S_n \colon n \geq 0\}$ is a simple symmetric random walk started at zero. We provide an alternative proof of the LDP via coupling to Brownian motion, and subsequent derivation of the LDP for a continuous-time analog of L. Finally, we turn our attention back to the urn process conditioned to be balanced, and provide a functional limit law describing the trajectory of the urn process.

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3

Haslegrave, John, and Jonathan Jordan. "Preferential attachment with choice." Random Structures & Algorithms 48, no. 4 (November 28, 2015): 751–66. http://dx.doi.org/10.1002/rsa.20616.

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4

Chen, Chen. "The origin of preferential attachment and the generalized preferential attachment for weighted networks." Physica A: Statistical Mechanics and its Applications 377, no. 2 (April 2007): 709–16. http://dx.doi.org/10.1016/j.physa.2006.11.082.

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5

Wu, Yan, Tom Z. J. Fu, and Dah Ming Chiu. "Generalized preferential attachment considering aging." Journal of Informetrics 8, no. 3 (July 2014): 650–58. http://dx.doi.org/10.1016/j.joi.2014.06.002.

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6

ANTUNOVIĆ, TONĆI, ELCHANAN MOSSEL, and MIKLÓS Z. RÁCZ. "Coexistence in Preferential Attachment Networks." Combinatorics, Probability and Computing 25, no. 6 (February 9, 2016): 797–822. http://dx.doi.org/10.1017/s0963548315000383.

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We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses neighbours by preferential attachment, and selects its type based on the number of initial neighbours of each type. The model is analysed in detail, and in particular, we determine the possible proportions of the various types in the limit of large networks. An important qualitative feature we find is that, in contrast to many current theoretical models, often several competitors will coexist. This matches empirical observations in many real-world networks.

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7

de Blasio, B. F., A. Svensson, and F. Liljeros. "Preferential attachment in sexual networks." Proceedings of the National Academy of Sciences 104, no. 26 (June 19, 2007): 10762–67. http://dx.doi.org/10.1073/pnas.0611337104.

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8

Garavaglia, Alessandro, and Clara Stegehuis. "Subgraphs in preferential attachment models." Advances in Applied Probability 51, no. 03 (September 2019): 898–926. http://dx.doi.org/10.1017/apr.2019.36.

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AbstractWe consider subgraph counts in general preferential attachment models with power-law degree exponent $\tau > 2$ . For all subgraphs H, we find the scaling of the expected number of subgraphs as a power of the number of vertices. We prove our results on the expected number of subgraphs by defining an optimization problem that finds the optimal subgraph structure in terms of the indices of the vertices that together span it and by using the representation of the preferential attachment model as a Pólya urn model.

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9

Lim, Chjan, and Weituo Zhang. "Relevance and Importance Preferential Attachment." Complex Systems 28, no. 3 (October 15, 2019): 333–56. http://dx.doi.org/10.25088/complexsystems.28.3.333.

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10

Lehmann, S., A. D. Jackson, and B. Lautrup. "Life, death and preferential attachment." Europhysics Letters (EPL) 69, no. 2 (January 2005): 298–303. http://dx.doi.org/10.1209/epl/i2004-10331-2.

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11

Zuev, Konstantin, Fragkiskos Papadopoulos, and Dmitri Krioukov. "Hamiltonian dynamics of preferential attachment." Journal of Physics A: Mathematical and Theoretical 49, no. 10 (January 27, 2016): 105001. http://dx.doi.org/10.1088/1751-8113/49/10/105001.

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12

Hruz, Tomas, and Ueli Peter. "Nongrowing Preferential Attachment Random Graphs." Internet Mathematics 6, no. 4 (March 9, 2011): 461–87. http://dx.doi.org/10.1080/15427951.2010.553143.

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13

Dommers, Sander, Remco van der Hofstad, and Gerard Hooghiemstra. "Diameters in Preferential Attachment Models." Journal of Statistical Physics 139, no. 1 (January 22, 2010): 72–107. http://dx.doi.org/10.1007/s10955-010-9921-z.

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14

Tameirão, Cinthya Rocha, Sérgio Fernando Loureiro Rezende, and Luciana Pereira de Assis. "Preferential Attachment and Fitness in the Evolution of the Brazilian Film Network." Organizações & Sociedade 28, no. 99 (December 2021): 888–916. http://dx.doi.org/10.1590/1984-92302021v28n9907en.

Full text

Abstract:

Abstract This study analyzes the network evolution, specifically that of the Brazilian film network. It examines two generative mechanisms that lie behind the network evolution: preferential attachment and fitness. The starting point is that preferential attachment and fitness may compete to shape the network evolution. We built a novel dataset with 974 Brazilian feature films released between 1995 and 2017 and used PAFit, a brand-new statistical method, to estimate the joint effects of preferential attachment and fitness on the evolution of the Brazilian film network. This study concludes that the network evolution is shaped by both preferential attachment and fitness. However, in the presence of fitness, the effects of preferential attachment on the network evolution become weaker. This means that the node ability to form ties in the Brazilian film network is mainly explained by its fitness. Besides, the preferential attachment assumes a sub-linear form. Costs, communication and managerial capabilities, and node age explain why nodes are unable to accumulate ties at rates proportional to their degree. Finally, preferential attachment and fitness manifest themselves heterogeneously, depending on either the type or the duration of the network. Preferential attachment drives the cast network evolution, whereas fitness is the main generative mechanism of the crew network. Actors and actresses rely on their status, privilege, and power to obtain future contracts (preferential attachment), whereas technical members are selected on the basis of their talent, skills, and knowledge (fitness). Due to node age or exit, preferential attachment becomes stronger in shorter networks.

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15

Rezaei, Soghra, Hanieh Moghaddasi, and Amir Hossein Darooneh. "Preferential attachment in evolutionary earthquake networks." Physica A: Statistical Mechanics and its Applications 495 (April 2018): 172–79. http://dx.doi.org/10.1016/j.physa.2017.12.063.

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16

Kasthurirathna, Dharshana, and Mahendra Piraveenan. "Cyclic Preferential Attachment in Complex Networks." Procedia Computer Science 18 (2013): 2086–94. http://dx.doi.org/10.1016/j.procs.2013.05.378.

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17

Weaver, Iain S. "Preferential attachment in randomly grown networks." Physica A: Statistical Mechanics and its Applications 439 (December 2015): 85–92. http://dx.doi.org/10.1016/j.physa.2015.06.019.

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18

Borrel, V., M. Dias de Amorim, and S. Fdida. "A preferential attachment gathering mobility model." IEEE Communications Letters 9, no. 10 (October 2005): 900–902. http://dx.doi.org/10.1109/lcomm.2005.10023.

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19

Hansen, Jennie C., and Jerzy Jaworski. "A random mapping with preferential attachment." Random Structures and Algorithms 34, no. 1 (January 2009): 87–111. http://dx.doi.org/10.1002/rsa.20251.

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20

Jeong, H., Z. Néda, and A. L. Barabási. "Measuring preferential attachment in evolving networks." Europhysics Letters (EPL) 61, no. 4 (February 2003): 567–72. http://dx.doi.org/10.1209/epl/i2003-00166-9.

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21

Wan, Phyllis, Tiandong Wang, Richard A. Davis, and Sidney I. Resnick. "Fitting the linear preferential attachment model." Electronic Journal of Statistics 11, no. 2 (2017): 3738–80. http://dx.doi.org/10.1214/17-ejs1327.

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22

Ben-Naim, E., and P. L. Krapivsky. "Stratification in the preferential attachment network." Journal of Physics A: Mathematical and Theoretical 42, no. 47 (November 4, 2009): 475001. http://dx.doi.org/10.1088/1751-8113/42/47/475001.

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23

Raigorodskii, A. M. "Small subgraphs in preferential attachment networks." Optimization Letters 11, no. 2 (September 9, 2015): 249–57. http://dx.doi.org/10.1007/s11590-015-0945-9.

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24

Малышкин, Юрий Андреевич. "PREFERENTIAL ATTACHMENT WITH FITNESS DEPENDENT CHOICE." Physical and Chemical Aspects of the Study of Clusters, Nanostructures and Nanomaterials, no. 13 (December 23, 2021): 483–94. http://dx.doi.org/10.26456/pcascnn/2021.13.483.

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Исследуется асимптотическое поведение максимальной степени вершины в графе предпочтительного присоединения с выбором вершины, основанном как на ее степени, так и на дополнительном параметре (пригодности). Модели предпочтительного присоединения широко используются для моделирования сложных сетей (таких как нейронные сети и т.д.). Они строятся следующим образом. Мы начинаем с двух вершин и ребра между ними. Затем на каждом шаге мы рассматриваем выборку из уже существующих вершин, выбранных с вероятностями, пропорциональными их степеням плюс некоторый параметр β>- 1. Затем мы добавляем новую вершину и соединяем ее ребром с вершиной из выборки, на которой достигается максимум произведения ее степени на ее пригодность. Мы доказали, что в зависимости от параметров модели возможны три типа поведения максимальной степени вершины - сублинейное, линейное и порядка /ln , где n - число вершин в графе. We study the asymptotic behavior of the maximum degree in the preferential attachment tree model with a choice based on both the degree and fitness of a vertex. The preferential attachment models are natural models for complex networks (like neural networks, etc.) and constructed in the following recursive way. To each vertex is assigned a parameter that is called a fitness of a vertex. We start from two vertices and an edge between them. On each step, we consider a sample with repetition of d vertices, chosen with probabilities proportional to their degrees plus some parameter β>-1. Then we add a new vertex and draw an edge from it to the vertex from the sample with the highest product of fitness and degree. We prove that the maximum degree, dependent on parameters of the model, could exhibit three types of asymptotic behavior: sublinear, linear, and of /ln order, where n is the number of edges in the graph.

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25

Siew, Cynthia S. Q., and Michael S. Vitevitch. "Investigating the Influence of Inverse Preferential Attachment on Network Development." Entropy 22, no. 9 (September 15, 2020): 1029. http://dx.doi.org/10.3390/e22091029.

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Recent work investigating the development of the phonological lexicon, where edges between words represent phonological similarity, have suggested that phonological network growth may be partly driven by a process that favors the acquisition of new words that are phonologically similar to several existing words in the lexicon. To explore this growth mechanism, we conducted a simulation study to examine the properties of networks grown by inverse preferential attachment, where new nodes added to the network tend to connect to existing nodes with fewer edges. Specifically, we analyzed the network structure and degree distributions of artificial networks generated via either preferential attachment, an inverse variant of preferential attachment, or combinations of both network growth mechanisms. The simulations showed that network growth initially driven by preferential attachment followed by inverse preferential attachment led to densely-connected network structures (i.e., smaller diameters and average shortest path lengths), as well as degree distributions that could be characterized by non-power law distributions, analogous to the features of real-world phonological networks. These results provide converging evidence that inverse preferential attachment may play a role in the development of the phonological lexicon and reflect processing costs associated with a mature lexicon structure.

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26

QIN, QIONG, ZHIPING WANG, FANG ZHANG, and PENGYUAN XU. "EVOLVING SCALE-FREE NETWORK MODEL." International Journal of Modern Physics B 22, no. 13 (May 20, 2008): 2139–49. http://dx.doi.org/10.1142/s0217979208039307.

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The Barabási–Albert (BA) model is extended here to include the concept of modifying the preferential attachment and combining the global preferential attachment with local preferential attachment. Our preferential attachment makes the nodes with higher degree increase less rapidly than the BA model after a long time. The maximum degree is introduced. We compare the time-evolution of the degree of the BA model and our model to illustrate that our model can control the degree of some nodes increasing dramatically with increasing time. Using the continuum theory and the rate equation method, we obtain the analytical expressions of the time-evolution of the degree and the power-law degree distribution.

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27

SANTIAGO, A., and R. M. BENITO. "EMERGENCE OF MULTISCALING IN HETEROGENEOUS COMPLEX NETWORKS." International Journal of Modern Physics C 18, no. 10 (October 2007): 1591–607. http://dx.doi.org/10.1142/s0129183107011571.

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In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the threshold model, a preferential attachment model where the affinity between node states biases the attachment probabilities of links. We show that the degree densities exhibit a power-law multiscaling which points to a signature of heterogeneity in preferential attachment networks. This translates into a power-law scaling in the degree distribution, whose exponent depends on the specific form of heterogeneity in the attachment mechanism.

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28

Lachgar, A., and A. Achahbar. "Network growth with preferential attachment and without “rich get richer” mechanism." International Journal of Modern Physics C 27, no. 02 (December 23, 2015): 1650020. http://dx.doi.org/10.1142/s0129183116500200.

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We propose a simple preferential attachment model of growing network using the complementary probability of Barabási–Albert (BA) model, i.e. [Formula: see text]. In this network, new nodes are preferentially attached to not well connected nodes. Numerical simulations, in perfect agreement with the master equation solution, give an exponential degree distribution. This suggests that the power law degree distribution is a consequence of preferential attachment probability together with “rich get richer” phenomena. We also calculate the average degree of a target node at time t[Formula: see text] and its fluctuations, to have a better view of the microscopic evolution of the network, and we also compare the results with BA model.

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29

Baur, Michael, Marco Gaertler, Robert Görke, Marcus Krug, and Dorothea Wagner. "Augmenting $k$-core generation with preferential attachment." Networks & Heterogeneous Media 3, no. 2 (2008): 277–94. http://dx.doi.org/10.3934/nhm.2008.3.277.

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30

Jordan, Jonathan. "Degree sequences of geometric preferential attachment graphs." Advances in Applied Probability 42, no. 02 (June 2010): 319–30. http://dx.doi.org/10.1017/s0001867800004079.

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We investigate the degree sequence of the geometric preferential attachment model of Flaxman, Frieze and Vera (2006), (2007) in the case where the self-loop parameter α is set to 0. We show that, given certain conditions on the attractiveness function F, the degree sequence converges to the same sequence as found for standard preferential attachment in Bollobás et al. (2001). We also apply our method to the extended model introduced in van der Esker (2008) which allows for an initial attractiveness term, proving similar results.

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31

Takei, Masato. "Preferential Attachment Models and Reinforced Random Walks." Brain & Neural Networks 21, no. 4 (2014): 170–81. http://dx.doi.org/10.3902/jnns.21.170.

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32

Jian-Jun, Wu, Gao Zi-You, Sun Hui-Jun, and Huang Hai-Jun. "Random and Preferential Attachment Networks with Aging." Chinese Physics Letters 22, no. 3 (February 24, 2005): 765–68. http://dx.doi.org/10.1088/0256-307x/22/3/068.

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33

Poncela, Julia, Jesús Gómez-Gardeñes, Luis M. Floría, Angel Sánchez, and Yamir Moreno. "Complex Cooperative Networks from Evolutionary Preferential Attachment." PLoS ONE 3, no. 6 (June 18, 2008): e2449. http://dx.doi.org/10.1371/journal.pone.0002449.

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34

D'Souza, R. M., C. Borgs, J. T. Chayes, N. Berger, and R. D. Kleinberg. "Emergence of tempered preferential attachment from optimization." Proceedings of the National Academy of Sciences 104, no. 15 (March 29, 2007): 6112–17. http://dx.doi.org/10.1073/pnas.0606779104.

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35

Prokhorenkova, L. A., and A. V. Krot. "Local clustering coefficients in preferential attachment models." Doklady Mathematics 94, no. 3 (November 2016): 623–26. http://dx.doi.org/10.1134/s1064562416060041.

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36

Lyon, Merritt R., and Hosam M. Mahmoud. "Trees grown under young-age preferential attachment." Journal of Applied Probability 57, no. 3 (September 2020): 911–27. http://dx.doi.org/10.1017/jpr.2020.49.

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AbstractWe introduce a class of non-uniform random recursive trees grown with an attachment preference for young age. Via the Chen–Stein method of Poisson approximation, we find that the outdegree of a node is characterized in the limit by ‘perturbed’ Poisson laws, and the perturbation diminishes as the node index increases. As the perturbation is attenuated, a pure Poisson limit ultimately emerges in later phases. Moreover, we derive asymptotics for the proportion of leaves and show that the limiting fraction is less than one half. Finally, we study the insertion depth in a random tree in this class. For the insertion depth, we find the exact probability distribution, involving Stirling numbers, and consequently we find the exact and asymptotic mean and variance. Under appropriate normalization, we derive a concentration law and a limiting normal distribution. Some of these results contrast with their counterparts in the uniform attachment model, and some are similar.

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37

Wang, Li-Na, Jin-Li Guo, Han-Xin Yang, and Tao Zhou. "Local preferential attachment model for hierarchical networks." Physica A: Statistical Mechanics and its Applications 388, no. 8 (April 2009): 1713–20. http://dx.doi.org/10.1016/j.physa.2008.12.028.

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38

Chrysafis, O., and C. Cannings. "Weighted self-similar networks under preferential attachment." Physica A: Statistical Mechanics and its Applications 388, no. 14 (July 2009): 2965–74. http://dx.doi.org/10.1016/j.physa.2009.03.030.

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39

Dai, Meifeng, Qi Xie, and Lei Li. "Dynamic weight evolution network with preferential attachment." Physica A: Statistical Mechanics and its Applications 416 (December 2014): 149–56. http://dx.doi.org/10.1016/j.physa.2014.08.049.

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40

Yudina, M. N. "Preferential attachment graphs as agent interaction structure." Journal of Physics: Conference Series 1441 (January 2020): 012176. http://dx.doi.org/10.1088/1742-6596/1441/1/012176.

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41

Dereich, Steffen, and Peter Mörters. "Random Networks with Concave Preferential Attachment Rule." Jahresbericht der Deutschen Mathematiker-Vereinigung 113, no. 1 (November 26, 2010): 21–40. http://dx.doi.org/10.1365/s13291-010-0011-6.

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42

Hajek, Bruce, and Suryanarayana Sankagiri. "Community Recovery in a Preferential Attachment Graph." IEEE Transactions on Information Theory 65, no. 11 (November 2019): 6853–74. http://dx.doi.org/10.1109/tit.2019.2927624.

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43

Jordan, Jonathan. "Degree sequences of geometric preferential attachment graphs." Advances in Applied Probability 42, no. 2 (June 2010): 319–30. http://dx.doi.org/10.1239/aap/1275055230.

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We investigate the degree sequence of the geometric preferential attachment model of Flaxman, Frieze and Vera (2006), (2007) in the case where the self-loop parameter α is set to 0. We show that, given certain conditions on the attractiveness function F, the degree sequence converges to the same sequence as found for standard preferential attachment in Bollobás et al. (2001). We also apply our method to the extended model introduced in van der Esker (2008) which allows for an initial attractiveness term, proving similar results.

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44

Flaxman, Abraham D., Alan M. Frieze, and Juan Vera. "A Geometric Preferential Attachment Model of Networks." Internet Mathematics 3, no. 2 (January 2006): 187–205. http://dx.doi.org/10.1080/15427951.2006.10129124.

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45

Ruiz, Diego, Juan Campos, and Jorge Finke. "Dynamics in Affinity-Weighted Preferential Attachment Networks." Journal of Statistical Physics 181, no. 2 (July 3, 2020): 673–89. http://dx.doi.org/10.1007/s10955-020-02594-0.

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46

SANTIAGO, ANTONIO, and ROSA M. BENITO. "EVOLUTION OF HETEROGENEOUS NETWORKS UNDER PREFERENTIAL ATTACHMENT." International Journal of Bifurcation and Chaos 20, no. 03 (March 2010): 923–27. http://dx.doi.org/10.1142/s0218127410026216.

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In this paper, we present results concerning a natural extension of the class of heterogeneous preferential attachment models, a generalization of the Barabási–Albert model to heterogeneous networks. In this extended class, the network nodes enjoy a nonzero attractiveness even when their connectivity degrees are zero. We analytically show that the degree densities of models in the extended class exhibit a richer scaling behavior than their homogeneous counterparts, and that power-law scaling in their degree distribution is robust in the presence of the offset in the attachment kernel.

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47

SHAO, CHEN-XI, HUI-LING DOU, RONG-XU YANG, and BING-HONG WANG. "ZERO NODES EFFECT: VALID LINK PREDICTION IN SPARSE NETWORKS." International Journal of Modern Physics B 27, no. 12 (April 29, 2013): 1350052. http://dx.doi.org/10.1142/s0217979213500525.

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Zero-degree nodes are an important difficulty in sparse networks' link prediction. Clustering and preferential attachment, as the most important characteristics of complex networks, have been paid little attention in similarity indices. Inspired by the coexistence of clustering and preferential attachment in real networks, this paper proposes a new preferential attachment index and new clustering index, which have here been integrated into a hybrid index that considers the dynamic evolutionary forces of complex networks and can solve the problem of excessive zero-degree nodes in sparse networks and check evolution mechanism. Experiments proved prediction accuracy can be remarkably enhanced.

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48

JANSON, SVANTE. "Random Recursive Trees and Preferential Attachment Trees are Random Split Trees." Combinatorics, Probability and Computing 28, no. 1 (May 21, 2018): 81–99. http://dx.doi.org/10.1017/s0963548318000226.

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We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree and the standard preferential attachment tree. An application is given to the sum over all pairs of nodes of the common number of ancestors.

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49

Rak, Rafał, and Ewa Rak. "The Fractional Preferential Attachment Scale-Free Network Model." Entropy 22, no. 5 (April 29, 2020): 509. http://dx.doi.org/10.3390/e22050509.

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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.

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Ruiz, Diego, and Jorge Finke. "Lyapunov–based Anomaly Detection in Preferential Attachment Networks." International Journal of Applied Mathematics and Computer Science 29, no. 2 (June 1, 2019): 363–73. http://dx.doi.org/10.2478/amcs-2019-0027.

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Abstract:

Abstract Network models aim to explain patterns of empirical relationships based on mechanisms that operate under various principles for establishing and removing links. The principle of preferential attachment forms a basis for the well-known Barabási–Albert model, which describes a stochastic preferential attachment process where newly added nodes tend to connect to the more highly connected ones. Previous work has shown that a wide class of such models are able to recreate power law degree distributions. This paper characterizes the cumulative degree distribution of the Barabási–Albert model as an invariant set and shows that this set is not only a global attractor, but it is also stable in the sense of Lyapunov. Stability in this context means that, for all initial configurations, the cumulative degree distributions of subsequent networks remain, for all time, close to the limit distribution. We use the stability properties of the distribution to design a semi-supervised technique for the problem of anomalous event detection on networks.

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