scholarly journals Correlation of automorphism group size and topological properties with program-size complexity evaluations of graphs and complex networks

2014 ◽  
Vol 404 ◽  
pp. 341-358 ◽  
Author(s):  
Hector Zenil ◽  
Fernando Soler-Toscano ◽  
Kamaludin Dingle ◽  
Ard A. Louis
Keyword(s):  
Automorphism Group ◽  
Complex Networks ◽  
Group Size ◽  
Topological Properties

scholarly journals Small world in a seismic network: the California case

2008 ◽  
Vol 15 (3) ◽  
pp. 389-395 ◽  
Author(s):  
A. Jiménez ◽  
K. F. Tiampo ◽  
A. M. Posadas
Keyword(s):  
Complex Networks ◽  
Recent Work ◽  
Brain Activity ◽  
Social Systems ◽  
Small World ◽  
Functional Networks ◽  
Topological Properties ◽  
Southern California Region ◽  
Seismic Area ◽  
The Brain

Abstract. Recent work has shown that disparate systems can be described as complex networks i.e. assemblies of nodes and links with nontrivial topological properties. Examples include technological, biological and social systems. Among them, earthquakes have been studied from this perspective. In the present work, we divide the Southern California region into cells of 0.1°, and calculate the correlation of activity between them to create functional networks for that seismic area, in the same way that the brain activity is studied from the complex network perspective. We found that the network shows small world features.

scholarly journals On the effects of memory and topology on the controllability of complex dynamical networks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Panagiotis Kyriakis ◽  
Sérgio Pequito ◽  
Paul Bogdan
Keyword(s):  
Complex Networks ◽  
Temporal Dynamics ◽  
Complex Dynamical Networks ◽  
Long Term Memory ◽  
Topological Properties ◽  
Control Effort ◽  
Dynamical Networks ◽  
Term Memory ◽  
Minimum Number

Abstract Recent advances in network science, control theory, and fractional calculus provide us with mathematical tools necessary for modeling and controlling complex dynamical networks (CDNs) that exhibit long-term memory. Selecting the minimum number of driven nodes such that the network is steered to a prescribed state is a key problem to guarantee that complex networks have a desirable behavior. Therefore, in this paper, we study the effects of long-term memory and of the topological properties on the minimum number of driven nodes and the required control energy. To this end, we introduce Gramian-based methods for optimal driven node selection for complex dynamical networks with long-term memory and by leveraging the structure of the cost function, we design a greedy algorithm to obtain near-optimal approximations in a computationally efficiently manner. We investigate how the memory and topological properties influence the control effort by considering Erdős–Rényi, Barabási–Albert and Watts–Strogatz networks whose temporal dynamics follow a fractional order state equation. We provide evidence that scale-free and small-world networks are easier to control in terms of both the number of required actuators and the average control energy. Additionally, we show how our method could be applied to control complex networks originating from the human brain and we discover that certain brain cortex regions have a stronger impact on the controllability of network than others.

scholarly journals Characterization of Symmetry of Complex Networks

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 692
Author(s):  
Yangyang Chen ◽  
Yi Zhao ◽  
Xinyu Han
Keyword(s):  
Automorphism Group ◽  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Symmetry Property ◽  
Global Symmetry ◽  
Quantitative Characterization ◽  
Natural Action ◽  
Vertex Set

Recently, symmetry in complex network structures has attracted some research interest. One of the fascinating problems is to give measures of the extent to which the network is symmetric. In this paper, based on the natural action of the automorphism group Aut ( Γ ) of Γ on the vertex set V of a given network Γ = Γ ( V , E ) , we propose three indexes for the characterization of the global symmetry of complex networks. Using these indexes, one can get a quantitative characterization of how symmetric a network is and can compare the symmetry property of different networks. Moreover, we compare these indexes to some existing ones in the literature and apply these indexes to real-world networks, concluding that real-world networks are far from vertex symmetric ones.

scholarly journals Computational Analysis of Imbalance-Based Irregularity Indices of Boron Nanotubes

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 678
Author(s):  
Yang ◽  
Munir ◽  
Rafique ◽  
Ahmad ◽  
Liu
Keyword(s):  
Molecular Structure ◽  
Statistical Analysis ◽  
Complex Networks ◽  
Computational Analysis ◽  
Chemical Properties ◽  
Molecular Topology ◽  
Topological Properties ◽  
Boiling Points ◽  
Boron Nanotube ◽  
Heats Of Vaporization

. Molecular topology provides a basis for the correlation of physical as well as chemical properties of a certain molecule. Irregularity indices are used as functions in the statistical analysis of the topological properties of certain molecular graphs and complex networks, and hence help us to correlate properties like enthalpy, heats of vaporization, and boiling points etc. with the molecular structure. In this article we are interested in formulating closed forms of imbalance-based irregularity measures of boron nanotubes. These tubes are known as α-boron nanotube, triangular boron nanotubes, and tri-hexagonal boron nanotubes. We also compare our results graphically and come up with the conclusion that alpha boron tubes are the most irregular with respect to most of the irregularity indices.

scholarly journals Bootstrapping Topological Properties and Systemic Risk of Complex Networks Using the Fitness Model

2013 ◽  
Vol 151 (3-4) ◽  
pp. 720-734 ◽  
Author(s):  
Nicolò Musmeci ◽  
Stefano Battiston ◽  
Guido Caldarelli ◽  
Michelangelo Puliga ◽  
Andrea Gabrielli
Keyword(s):  
Complex Networks ◽  
Systemic Risk ◽  
Topological Properties

On the augmentation topology of automorphism groups of affine spaces and algebras

2018 ◽  
Vol 28 (08) ◽  
pp. 1449-1485 ◽  
Author(s):  
Alexei Kanel-Belov ◽  
Jie-Tai Yu ◽  
Andrey Elishev
Keyword(s):  
Automorphism Group ◽  
Associative Algebra ◽  
Automorphism Groups ◽  
Jacobian Conjecture ◽  
Free Associative Algebra ◽  
Topological Properties ◽  
Negative Solution ◽  
Base Field ◽  
Associative Algebras ◽  
Affine Spaces

We study topological properties of Ind-groups [Formula: see text] and [Formula: see text] of automorphisms of polynomial and free associative algebras via Ind-schemes, toric varieties, approximations, and singularities. We obtain a number of properties of [Formula: see text], where [Formula: see text] is the polynomial or free associative algebra over the base field [Formula: see text]. We prove that all Ind-scheme automorphisms of [Formula: see text] are inner for [Formula: see text], and all Ind-scheme automorphisms of [Formula: see text] are semi-inner. As an application, we prove that [Formula: see text] cannot be embedded into [Formula: see text] by the natural abelianization. In other words, the Automorphism Group Lifting Problem has a negative solution. We explore close connection between the above results and the Jacobian conjecture, as well as the Kanel-Belov–Kontsevich conjecture, and formulate the Jacobian conjecture for fields of any characteristic. We make use of results of Bodnarchuk and Rips, and we also consider automorphisms of tame groups preserving the origin and obtain a modification of said results in the tame setting.

scholarly journals Reconstructing Topological Properties of Complex Networks Using the Fitness Model

2015 ◽  
pp. 323-333 ◽  
Author(s):  
Giulio Cimini ◽  
Tiziano Squartini ◽  
Nicolò Musmeci ◽  
Michelangelo Puliga ◽  
Andrea Gabrielli ◽  
...  
Keyword(s):  
Complex Networks ◽  
Topological Properties

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 A fractal hypernetwork model with good controllability

2021 ◽  
Vol 6 (12) ◽  
pp. 13758-13773
Author(s):  
Xiujuan Ma ◽  
◽  
Fuxiang Ma ◽  
Jun Yin ◽  
Keyword(s):  
Complex Networks ◽  
Exact Controllability ◽  
Topological Properties ◽  
Topology Structure ◽  
Fractal Properties ◽  
Simulation Results ◽  
Interesting Structure

<abstract> <p>Fractal is a common feature of many deterministic complex networks. The complex networks with fractal features have interesting structure and good performance. The network based on hypergraph is named hypernetwork. In this paper, we construct a hypernetwork model with fractal properties, and obtain its topological properties. Moreover, according to the exact controllability theory, we obtain the node controllability and the hyperedge controllability of the fractal hypernetwork. The simulation results show that the measure of hyperedge controllability is smaller than that of node in the fractal hypernetwork. In addition, We compare the controllability of three types of hypernetwork, which are easier to control by their hyperedges. It is shown the fractal hypernetwork constructed in this paper has the best controllability. Because of the good controllability of our fractal hypernetwork model, it is suitable for the topology structure of many real systems.</p> </abstract>

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