Growth model for fractal scale-free networks generated by a random walk

Ikeda, Nobutoshi

doi:10.1016/j.physa.2019.01.043

Cited by 13 publications

(5 citation statements)

References 32 publications

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“…In recent years, the relationship between the small-world nature of complex networks and fractals has been discussed, particularly with regard to the World Web network, [30] brain networks, [31] and the tree algorithm (family tree) [32] and so on. Most complex networks in the real world exhibit small-world properties.…”

Section: Resultsmentioning

confidence: 99%

“…Most complex networks in the real world exhibit small-world properties. More precisely, the average node pair distance L in these cases is considered to be much smaller than the number of nodes N [30][31][32]. The application of a modified model that possesses these features will yield an understanding of nature because most of the fractal networks observed in the real world, such as the World Wide Web or metabolic networks, have a scalefree property.…”

Section: Resultsmentioning

confidence: 99%

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Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Munakata,

Ogiya,

Sato

2024

Appl. Phys. A

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To investigate the relationship between histological properties and thermal conductivities of binary self-assembled/self-organized fractal materials fabricated by the mixed diffusion of filler particles, the particle group distribution of the filler particles was analyzed. Unlike conventional research on particle size distribution, we performed an analysis that focuses on interactions and connectivity between particles from the perspective of the Barabasi-Albert model. In three complex network systems of β-Si3N4 (SN)/austenitic stainless steel (SUS), SN/piezoelectric polyvinylidene fluoride (PVDF), and BaTiO3 (BT)/PVDF, the size distribution of secondary particles was a power-law distribution until the particle group grew relatively large. In the SN/SUS and SN/PVDF systems, a crossover phenomenon was observed in which the order distribution exhibited a power-law in the region where the particle group area was small, and as the particle group became larger, the order distribution became exponential distribution. On the other hand, the BT/PVDF system deviated from the power law distribution as the particle group area increased but did not exhibit an exponential distribution. The characteristics of the particle group distribution of these filler particles were closely related to thermal conductivity, indicating that the connection of particle groups was important. Furthermore, the relationship between the multifractal capacitance dimension, which is strongly correlated with the distance between the particle groups, and the total number of filler particle groups suggests that the texture of these composite material systems may have both small-world and scale-free properties. We also focused on the relationship between the multifractal and complex network properties of the three particle groups. As a result, a correlation was found between the slope γ, which reflects the characteristics of the power distribution, and the thermodynamic parameter α (corresponding to internal energy change) obtained from multifractals. In particular, the smaller the change in γ relative to the change in α, the more pronounced the bonding of particles and particle groups, while the larger change in γ suggested the dispersion of particle groups.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Munakata,

Ogiya,

Sato

2024

Appl. Phys. A

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“…Many studies have considered the preferential attachment mechanism to cause scale-free networks. In contrast, nonpreferential attachment is proposed to explain some nonscale-free network [51][52][53]. A significant question is how to generate networks with high clustering coefficient, small-world, and scale-free characteristics.…”

Section: Discussionmentioning

confidence: 99%

Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties

Yan

2023

Journal of Applied Mathematics

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Networks are prevalent in real life, and the study of network evolution models is very important for understanding the nature and laws of real networks. The distribution of the initial degree of nodes in existing classical models is constant or uniform. The model we proposed shows binomial distribution, and it is consistent with real network data. The theoretical analysis shows that the proposed model is scale-free at different probability values and its clustering coefficients are adjustable, and the Barabasi-Albert model is a special case of p = 0 in our model. In addition, the analytical results of the clustering coefficients can be estimated using mean-field theory. The mean clustering coefficients calculated from the simulated data and the analytical results tend to be stable. The model also exhibits small-world characteristics and has good reproducibility for short distances of real networks. Our model combines three network characteristics, scale-free, high clustering coefficients, and small-world characteristics, which is a significant improvement over traditional models with only a single or two characteristics. The theoretical analysis procedure can be used as a theoretical reference for various network models to study the estimation of clustering coefficients. The existence of stable equilibrium points of the model explains the controversy of whether scale-free is universal or not, and this explanation provides a new way of thinking to understand the problem.

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“…In fact, there have been a great deal of treelike models proposed to model many complex networks. Hence a number of their topological structure properties have been reported, for instance, geodesic distance [9], mean first-passage time for random walk [10], fractal phenomena [11] and so on.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for geodesic distance on treelike models with some constraints

Luo¹,

Ma²,

Xu³

2019

Preprint

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Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few decades, particularly, almost all data structures and corresponding algorithms suitable to searching information generated based on treelike models. Hence, we, in this paper, study in detail geodesic distance on some treelike models which can be generated by three different types of operations, including first-order subdivision, (1, m)-star-fractal operation and m-vertex-operation. Compared to the most best used approaches for calculating geodesic distance on graphs, for instance, enumeration method and matrix multiplication, we take useful advantage of a novel method consisting in spirit of the concept of vertex cover in the language of graph theory and mapping. For each kind of treelike model addressed here, we certainly obtain an exact solution for its geodesic distance using our method. With the help of computer simulations, we confirm that the analytical results are in perfect agreement with simulations. In addition, we also report some intriguing structure properties on treelike models of two types among them. The one obeys exponential degree distribution seen in many complex networks, by contrast, the other possesses all but leaf vertices with identical degree and shows more homogeneous topological structure than the former. Besides that, the both have, in some sense, self-similar feature but instead the latter exhibits fractal property.

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Growth model for fractal scale-free networks generated by a random walk

Cited by 13 publications

References 32 publications

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties

Exact solutions for geodesic distance on treelike models with some constraints

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