Connectivity degrees in the threshold preferential attachment model

Santiago, A.; Benito, R. M.

doi:10.1016/j.physa.2007.12.010

Cited by 11 publications

(7 citation statements)

References 38 publications

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“…In other words, the degree distribution P(k) of a network measures the probability of finding a node with connectivity degree k in the network. Alternatively, the product NP(k) measures the average number of nodes in the network with a given connectivity degree k (Santiago and Benito, 2007b). Figure 5 shows the degree k histograms.…”

Section: Model Resultsmentioning

confidence: 99%

“…In this model, we interpret porous soils as heterogeneous networks where pores are abstracted as nodes, characterized by their size and spatial location, and the links representing connections between them. The networks of pores are generated by a model known as the heterogeneous preferential attachment (HPA) (Santiago and Benito, 2007a, 2007b), a generalization of the Barabási-Albert model (Barabási and Albert, 1999) to heterogeneous networks. Developing an exhaustive analysis of the model, we obtained analytical solutions for the degree densities and degree distribution of the pore networks generated by the model approaching the limit of highest number of nodes (thermodynamic limit) and have shown that the networks can exhibit similar properties to those observed in other complex networks (Santiago and Benito, 2007a).…”

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confidence: 99%

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Community Structure in a Soil Porous System

Cárdenas¹,

Santiago²,

Tarquis³

et al. 2012

Soil Science

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Diffusion controls the gaseous transport process in soils when advective transport is almost null. Knowledge of the soil structure and pore connectivity are critical issues to understand and modelling soil aeration, sequestration or emission of greenhouse gasses, volatilization of volatile organic chemicals among other phenomena. In the last decades these issues increased our attention as scientist have realize that soil is one of the most complex materials on the earth, within which many biological, physical and chemical processes that support life and affect climate change take place.A quantitative and explicit characterization of soil structure is difficult because of the complexity of the pore space. This is the main reason why most theoretical approaches to soil porosity are idealizations to simplify this system. In this work, we proposed a more realistic attempt to capture the complexity of the system developing a model that considers the size and location of pores in order to relate them into a network. In the model we interpret porous soils as heterogeneous networks where pores are represented by nodes, characterized by their size and spatial location, and the links representing flows between them.In this work we perform an analysis of the community structure of porous media of soils represented as networks. For different real soils samples, modelled as heterogeneous complex networks, spatial communities of pores have been detected depending on the values of the parameters of the porous soil model used. These types of models are named as Heterogeneous Preferential Attachment (HPA). Developing an exhaustive analysis of the model, analytical solutions are obtained for the degree densities and degree distribution of the pore networks generated by the model in the thermodynamic limit and shown that the networks exhibit similar properties to those observed in other complex networks. With the aim to study in more detail topological properties of these networks, the presence of soil pore community structures is studied. The detection of communities of pores, as groups densely connected with only sparser connections between groups, could contribute to understand the mechanisms of the diffusion phenomena in soils.

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Section: Model Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Community Structure in a Soil Porous System

Cárdenas¹,

Santiago²,

Tarquis³

et al. 2012

Soil Science

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“…There are many parameters and values that can be chosen to represent and analyze networks [6][7][8][21][22][23][24][25][26][27][28][29][30][31][32]. For our simplest possible semantic network we sought the minimal set of measures needed to distinguish between fictional and non-fictional written storytelling, and found the power law exponents γ 1 , γ 2 , γ 3 to be optimal.…”

Section: A Fitting Methods and Fisher's Linear Discriminantmentioning

confidence: 99%

Distinguishing Fact from Fiction: Pattern Recognition in Texts Using Complex Networks

Stevanak,

Larue,

Carr

2010

Preprint

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We establish concrete mathematical criteria to distinguish between different kinds of written storytelling, fictional and non-fictional. Specifically, we constructed a semantic network from both novels and news stories, with N independent words as vertices or nodes, and edges or links allotted to words occurring within m places of a given vertex; we call m the word distance. We then used measures from complex network theory to distinguish between news and fiction, studying the minimal text length needed as well as the optimized word distance m. The literature samples were found to be most effectively represented by their corresponding power laws over degree distribution P (k) and clustering coefficient C(k); we also studied the mean geodesic distance, and found all our texts were small-world networks. We observed a natural break-point at k = √ N where the power law in the degree distribution changed, leading to separate power law fit for the bulk and the tail of P (k). Our linear discriminant analysis yielded a 73.8 ± 5.15% accuracy for the correct classification of novels and 69.1 ± 1.22% for news stories. We found an optimal word distance of m = 4 and a minimum text length of 100 to 200 words N .

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“…Master equations for evolution model with birth and death are analyzed by Alvarez-Martı´nez et al 9 As for preferential attachment, popular strategies include fitness model, 10,11 attractiveness model, 12,13 energy-aware model, 6,[14][15][16] and threshold preferential attachment model. 17 Moreover, Jin et al 18 proposed a survival topology evolution model in consideration of node survivability. A local-world model based on random walk and policy attachment is presented by Jiang.…”

Section: Introductionmentioning

confidence: 99%

A quality-of-service-aware dynamic evolution model for space–ground integrated network

Yi¹,

Du²,

Liao³

et al. 2017

International Journal of Distributed Sensor Networks

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Space-ground integrated network, a strategic, driving, and irreplaceable infrastructure, guarantees the development of economic and national security. However, its natures of limited resources, frequent handovers, and intermittently connected links significantly reduce the quality of service. To address this issue, a quality-of-service-aware dynamic evolution model is proposed based on complex network theory. On one hand, a quality-of-service-aware strategy is adopted in the model. During evolution phases of growth and handovers, links are established or deleted according to the qualityof-service-aware preferential attachment following the rule of better quality of service getting richer and worse quality of service getting poor or to die. On the other hand, dynamic handover of nodes and intermittent connection of links are taken into account and introduced into the model. Meanwhile, node heterogeneity is analyzed and heterogeneous nodes are endowed with discriminate interactions. Theoretical analysis and simulations are utilized to explore the degree distribution and its characteristics. Results reveal that this model is a scale-free model with drift power-law distribution, fat-tail and small-world effect, and drift character of degree distribution results from dynamic handover. Furthermore, this model exerts well fault tolerance and attack resistance compared to signal-strength-based strategy. In addition, node heterogeneity and quality-of-service-aware strategy improve the attack resistance and overall quality of service of space-ground integrated network.

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Connectivity degrees in the threshold preferential attachment model

Cited by 11 publications

References 38 publications

Community Structure in a Soil Porous System

Community Structure in a Soil Porous System

Distinguishing Fact from Fiction: Pattern Recognition in Texts Using Complex Networks

A quality-of-service-aware dynamic evolution model for space–ground integrated network

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