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

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 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.

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.

scholarly journals EMERGENCE OF MULTISCALING IN HETEROGENEOUS COMPLEX NETWORKS

2007 ◽  
Vol 18 (10) ◽  
pp. 1591-1607 ◽  
Author(s):  
A. SANTIAGO ◽  
R. M. BENITO
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Threshold Model ◽  
Specific Form ◽  
Numerical Evidence ◽  
Attachment Model ◽  
Attachment Mechanism

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.

scholarly journals On a growth model for complex networks capable of producing power-law out-degree distributions with wide range exponents

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
J. Esquivel-Gómez ◽  
P. D. Arjona-Villicaña ◽  
E. Stevens-Navarro ◽  
U. Pineda-Rico ◽  
R. E. Balderas-Navarro ◽  
...  
Keyword(s):  
Complex Networks ◽  
Growth Model ◽  
Power Law ◽  
Wide Range

The structural properties and the spanning trees entropy of the generalized Fractal Scale-Free Lattice

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Raihana Mokhlissi ◽  
Dounia Lotfi ◽  
Mohamed El Marraki ◽  
Joyati Debnath
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Power Law ◽  
Degree Distribution ◽  
Spanning Trees ◽  
Free Lattice ◽  
Scale Free ◽  
Computer Scientists ◽  
Electrical Engineers ◽  
Number Of Spanning Trees

Abstract Enumerating all the spanning trees of a complex network is theoretical defiance for mathematicians, electrical engineers and computer scientists. In this article, we propose a generalization of the Fractal Scale-Free Lattice and we study its structural properties. As its degree distribution follows a power law, we prove that the proposed generalization does not affect the scale-free property. In addition, we use the electrically equivalent transformations to count the number of spanning trees in the generalized Fractal Scale-Free Lattice. Finally, in order to evaluate the robustness of the generalized lattice, we compute and compare its entropy with other complex networks having the same average degree.

NECESSARY BACKBONE OF SUPERHIGHWAYS FOR TRANSPORT ON GEOGRAPHICAL COMPLEX NETWORKS

2009 ◽  
Vol 12 (01) ◽  
pp. 73-86 ◽  
Author(s):  
YUKIO HAYASHI
Keyword(s):  
Wireless Communication ◽  
Theoretical Prediction ◽  
Complex Networks ◽  
Shortest Path ◽  
Power Law ◽  
Degree Distribution ◽  
Topological Structure ◽  
Topological Properties ◽  
Scale Free ◽  
Law Degree

Many real networks have a common topological structure called scale-free (SF) that follows a power law degree distribution, and are embedded on an almost planar space which is suitable for wireless communication. However, the geographical constraints on local cycles cause more vulnerable connectivity against node removals, whose tolerance is reduced from the theoretical prediction under the assumption of uncorrelated locally tree-like structure. We consider a realistic generation of geographical networks with the SF property, and show the significant improvement of the robustness by adding a small fraction of shortcuts between randomly chosen nodes. Moreover, we quantitatively investigate the contribution of shortcuts to transport many packets on the shortest path for the spatially different amount of communication requests. Such a shortcut strategy preserves topological properties and a backbone naturally emerges bridging isolated clusters.

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