scholarly journals On the Emergence of Islands in Complex Networks

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
J. Esquivel-Gómez ◽  
R. E. Balderas-Navarro ◽  
P. D. Arjona-Villicaña ◽  
P. Castillo-Castillo ◽  
O. Rico-Trejo ◽  
...  
Keyword(s):  
Complex Networks ◽  
Size Distribution ◽  
Growth Model ◽  
Power Law ◽  
Degree Distribution ◽  
Growth Models ◽  
Island Size ◽  
First Case ◽  
Proposed Model ◽  
Power Law Function

Most growth models for complex networks consider networks comprising a single connected block or island, which contains all the nodes in the network. However, it has been demonstrated that some large complex networks have more than one island, with an island size distribution (Is) obeying a power-law function Is~s-α. This paper introduces a growth model that considers the emergence of islands as the network grows. The proposed model addresses the following two features: (i) the probability that a new island is generated decreases as the network grows and (ii) new islands are created with a constant probability at any stage of the growth. In the first case, the model produces an island size distribution that decays as a power-law Is~s-α with a fixed exponent α=1 and in-degree distribution that decays as a power-law Qi~i-γ with γ=2. When the second case is considered, the model describes island size and in-degree distributions that decay as a power-law with 2<α<∞ and 2<γ<∞, respectively.

scholarly journals A growth model for directed complex networks with power-law shape in the out-degree distribution

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
J. Esquivel-Gómez ◽  
E. Stevens-Navarro ◽  
U. Pineda-Rico ◽  
J. Acosta-Elias
Keyword(s):  
Complex Networks ◽  
Growth Model ◽  
Power Law ◽  
Degree Distribution

The moment ratios of particle size distributions in some simple growth models

1980 ◽  
Vol 17 (4) ◽  
pp. 956-967 ◽  
Author(s):  
H. L. MacGillivray
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Growth Model ◽  
Hazard Rate ◽  
Growth Models ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Initial Size ◽  
The Moment ◽  
Simple Growth

Important parameters of particle size distributions in dispersed systems in engineering and related fields are ratios of moments and inverse powers of these ratios, known as mean sizes. The variation in these parameters is examined for the simplest growth model in which the size distribution is translated, and the results for this process considered in relation to the problems of models of other growth processes. For initial size distributions with monotone hazard rate, the results are particularly significant, and the properties of the normalised moments of other distributions are also considered.

scholarly journals A Size-Perimeter Discrete Growth Model for Percolation Clusters

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Bendegúz Dezső Bak ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Growth Model ◽  
Branching Process ◽  
Growth Models ◽  
Square Lattice ◽  
Cluster Growth ◽  
Invasion Percolation ◽  
Percolation Clusters ◽  
Proposed Model ◽  
Wide Range ◽  
The Mean

Cluster growth models are utilized for a wide range of scientific and engineering applications, including modeling epidemics and the dynamics of liquid propagation in porous media. Invasion percolation is a stochastic branching process in which a network of sites is getting occupied that leads to the formation of clusters (group of interconnected, occupied sites). The occupation of sites is governed by their resistance distribution; the invasion annexes the sites with the least resistance. An iterative cluster growth model is considered for computing the expected size and perimeter of the growing cluster. A necessary ingredient of the model is the description of the mean perimeter as the function of the cluster size. We propose such a relationship for the site square lattice. The proposed model exhibits (by design) the expected phase transition of percolation models, i.e., it diverges at the percolation threshold p c . We describe an application for the porosimetry percolation model. The calculations of the cluster growth model compare well with simulation results.

The moment ratios of particle size distributions in some simple growth models

1980 ◽  
Vol 17 (04) ◽  
pp. 956-967 ◽  
Author(s):  
H. L. MacGillivray
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Growth Model ◽  
Hazard Rate ◽  
Growth Models ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Initial Size ◽  
The Moment ◽  
Simple Growth

Important parameters of particle size distributions in dispersed systems in engineering and related fields are ratios of moments and inverse powers of these ratios, known as mean sizes. The variation in these parameters is examined for the simplest growth model in which the size distribution is translated, and the results for this process considered in relation to the problems of models of other growth processes. For initial size distributions with monotone hazard rate, the results are particularly significant, and the properties of the normalised moments of other distributions are also considered.

DOUBLE POWER-LAW DEGREE DISTRIBUTION AND INFORMATIONAL ENTROPY IN URBAN ROAD NETWORKS

2011 ◽  
Vol 22 (01) ◽  
pp. 13-20 ◽  
Author(s):  
JIAN JIANG ◽  
FRÉDÉRIC METZ ◽  
CHRISTOPHE BECK ◽  
SÉBASTIEN LEFEVRE ◽  
JINCAN CHEN ◽  
...  
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Power Laws ◽  
Small Degree ◽  
Informational Entropy ◽  
Probabilistic Uncertainty ◽  
Urban Road ◽  
Information Measures ◽  
Power Law Function ◽  
Law Degree

The double power-law function, p(x) ~ 1/(xb + cxd) where x is the degree of one node, and b, c, d are parameters, is used to fit the degree distribution of urban road network of Le Mans city in France. It is called "double power-law" since it behaves as two power laws respectively, in large and small degree region with a crossing in-between. The position of the crossing point is derived as a function of the three parameters. The probabilistic uncertainty of this law is studied with two possible information measures: a generalized measure called varentropy and the Shannon entropy formula.

scholarly journals Preprocessing Rules for Target Set Selection in Complex Networks

2020 ◽  
Author(s):  
Renato Silva Melo ◽  
André Luís Vignatti
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Real World ◽  
Degree Distribution ◽  
Topological Properties ◽  
Input Graph ◽  
Target Set ◽  
Law Degree ◽  
Entire Network ◽  
Target Set Selection

In the Target Set Selection (TSS) problem, we want to find the minimum set of individuals in a network to spread information across the entire network. This problem is NP-hard, so find good strategies to deal with it, even for a particular case, is something of interest. We introduce preprocessing rules that allow reducing the size of the input without losing the optimality of the solution when the input graph is a complex network. Such type of network has a set of topological properties that commonly occurs in graphs that model real systems. We present computational experiments with real-world complex networks and synthetic power law graphs. Our strategies do particularly well on graphs with power law degree distribution, such as several real-world complex networks. Such rules provide a notable reduction in the size of the problem and, consequently, gains in scalability.

scholarly journals Polygon-Based Hierarchical Planar Networks Based on Generalized Apollonian Construction

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 998-1014
Author(s):  
Mikhail Tamm ◽  
Dmitry Koval ◽  
Vladimir Stadnichuk
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Scale Free ◽  
Model Network ◽  
Suggested Procedure ◽  
Similar Construction ◽  
Scale Free Graphs ◽  
Planar Networks

Experimentally observed complex networks are often scale-free, small-world and have an unexpectedly large number of small cycles. An Apollonian network is one notable example of a model network simultaneously having all three of these properties. This network is constructed by a deterministic procedure of consequentially splitting a triangle into smaller and smaller triangles. In this paper, a similar construction based on the consequential splitting of tetragons and other polygons with an even number of edges is presented. The suggested procedure is stochastic and results in the ensemble of planar scale-free graphs. In the limit of a large number of splittings, the degree distribution of the graph converges to a true power law with an exponent, which is smaller than three in the case of tetragons and larger than three for polygons with a larger number of edges. It is shown that it is possible to stochastically mix tetragon-based and hexagon-based constructions to obtain an ensemble of graphs with a tunable exponent of degree distribution. Other possible planar generalizations of the Apollonian procedure are also briefly discussed.

Particle size distribution and wastewater filter performance

1997 ◽  
Vol 36 (4) ◽  
pp. 217-224 ◽  
Author(s):  
Iris Kaminski ◽  
Nicolae Vescan ◽  
Avner Adin
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Power Law ◽  
Filter Performance ◽  
Natural Lakes ◽  
Size Groups ◽  
Filter Operation ◽  
Power Law Function ◽  
And Function

Particle size distribution (PSD) allows more accurate simulations of filtration models and better understanding of filter performance. PSD in municipal activated sludge effluent filtration is determined, varying filtration rate, grain size, flocculant type and dosage and function parameters are examined in this work. Results show, that removal efficiency varies for different size groups: small particles in the range of 5-10 μm in initialization stage, with no chemical aids, are poorly removed. Higher rate filters were more sensitive to the particle size than lower rate filters. Filtration with chemical aids is more sensitive to filtration conditions than filtration with no chemical additions. Particle size distribution in filtrate generally fits power law function behavior better than in raw effluent. The treatment smoothens the function somewhat. In a similar manner to the effect of settling in tanks or in natural lakes. Degree of correlation to power law function may indicate the mode of filter operation: high - working stage, low - breakthrough stage. β may also reflect on filters performance: high values - initial filtration stages. Decrease in β values - cycle progress towards breakthrough. Low β values, with low PSD correlation to power law function, may indicate low filtration efficiency or breakthrough.

scholarly journals Detecting different topologies immanent in scale-free networks with the same degree distribution

2019 ◽  
Vol 116 (14) ◽  
pp. 6701-6706 ◽  
Author(s):  
Dimitrios Tsiotas
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Network Topology ◽  
Degree Distribution ◽  
Growth Process ◽  
Preferential Attachment ◽  
Self Similarity ◽  
Scale Free ◽  
Scale Free Networks ◽  
Definition Of

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási−Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and lattice-like) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics.

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