Parameter specification for the degree distribution of simulated Barabási–Albert graphs

Mohd-Zaid, Fairul; Kabban, Christine M. Schubert; Deckro, Richard F.; White, Edward B.

doi:10.1016/j.physa.2016.07.024

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…This is not unexpected as Li et al 26 have observed that the preferential attachment model causes biases in the structure of the graph where high-degree nodes are interconnected, and Bubeck et al 27 have theoretically shown that the resulting graph of preferential attachment is very dependent on the starting graph. In addition, Mohd-Zaid et al 28 have empirically shown that the degree distribution of simulated BA networks does not follow the theoretical result originally derived by Barabási and Albert. 4 Therefore, we simulated another set of data to study the behavior of the bias in the expected value and variance and to derive a test for the scale-free property that corrects for this bias.…”

Section: Methodsmentioning

confidence: 88%

“…Due to the findings in Li et al, 26 Bubeck et al, 27 and Mohd-Zaid et al, 28 the power of the test for β 0 with the assumption that β 0 = 2 . 16 and 2.45 was also computed where the estimates for the correcting scalars were computed using the appropriate β 0 values. However, the result did not differ from when β 0 = 2 which suggests that the power of the test is invariant of β 0 and is strictly a function of the difference from β 0 .…”

Section: Methodsmentioning

confidence: 99%

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Network characterization and simulation via mixed properties of the Barabási–Albert and Erdös–Rényi degree distribution

Mohd-Zaid

Kabban

Deckro

et al. 2022

Journal of Defense Modeling & Simulation

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Social network analysis (SNA) is a tool for the operations researcher to understand, monitor, and exploit social and military structures which are key in the intelligence community. However, in order to study and influence a network of interest, the network must first be characterized; preferably to a known network model that captures a mixture of graphical properties exhibited by the social network of interest. In this work, we present a novel statistical method for both characterizing networks via a Binomial-Pareto maximum-likelihood approach and simulating the characterized network using a graph of mixed Barabási–Albert (BA, scale-free) and Erdös–Rényi (ER, randomness) properties. Characterization is performed through a combination of hypothesis tests and method of moments parameter estimation on Pareto and Doubly Truncated Binomial distributions. Application on real-world networks suggests that such networks may be characterized with a mixture of scale-free and random properties as modeled through BA and ER graphs. We demonstrate that our simulation methods are able to capture the degree distribution and density of the networks examined. These results demonstrate that this work establishes a statistical framework upon which network characterization and simulation may be accomplished, thus enabling the adaptation of such methods when generating, manipulating, and observing networks of interest.

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Section: Methodsmentioning

confidence: 88%

Section: Methodsmentioning

confidence: 99%

Network characterization and simulation via mixed properties of the Barabási–Albert and Erdös–Rényi degree distribution

Mohd-Zaid

Kabban

Deckro

et al. 2022

Journal of Defense Modeling & Simulation

Self Cite

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“…Watts and Strogatz [6] also defined the characteristic path length to measure the typical separation between two nodes in the network. In more recent years, numerous researches paid attention to degree distribution [7][8][9][10]. Early researches believed that degree distribution followed Poisson Distribution just as the random network theory has described [11,12].…”

Section: Introductionmentioning

confidence: 99%

High-Order Degree and Combined Degree in Complex Networks

Wang

Song

et al. 2018

Mathematical Problems in Engineering

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We define several novel centrality metrics: the high-order degree and combined degree of undirected network, the high-order out-degree and in-degree and combined out out-degree and in-degree of directed network. Those are the measurement of node importance with respect to the number of the node neighbors. We also explore those centrality metrics in the context of several best-known networks. We prove that both the degree centrality and eigenvector centrality are the special cases of the high-order degree of undirected network, and both the in-degree and PageRank algorithm without damping factor are the special cases of the high-order in-degree of directed network. Finally, we also discuss the significance of high-order out-degree of directed network. Our centrality metrics work better in distinguishing nodes than degree and reduce the computation load compared with either eigenvector centrality or PageRank algorithm.

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The impact of node arrival process and stochastic edge growth on scale-free distribution in complex networks

Safaei

Yeganloo

Moudi

2019

International Journal of Modelling and Simulation

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Parameter specification for the degree distribution of simulated Barabási–Albert graphs

Cited by 4 publications

References 17 publications

Network characterization and simulation via mixed properties of the Barabási–Albert and Erdös–Rényi degree distribution

Network characterization and simulation via mixed properties of the Barabási–Albert and Erdös–Rényi degree distribution

High-Order Degree and Combined Degree in Complex Networks

The impact of node arrival process and stochastic edge growth on scale-free distribution in complex networks

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