DEFINING DIMENSION OF A COMPLEX NETWORK

2007 ◽  
Vol 21 (06) ◽  
pp. 321-326 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Regular Lattices ◽  
Extensive Property ◽  
Definition Of

An important question in statistical mechanics is the dependence of model behavior on the dimension of the system. In this paper, we discuss extending the definition of dimension from regular lattices to complex networks. We use the definition to study how the extensive property of the power law potential exponent depends on dimension.

GRAPH ZETA FUNCTION AND DIMENSION OF COMPLEX NETWORK

2007 ◽  
Vol 21 (11) ◽  
pp. 639-644 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Zeta Function ◽  
Complex Network ◽  
System Behavior ◽  
Mathematical Properties ◽  
Scaling Property ◽  
Definition Of

In a recent paper we had defined the dimension of a complex network in terms of the scaling property of the volume. The question assumes significance because the dependence of system behavior on dimension is an important topic in statistical mechanics. Hence we consider the definition in more detail, and we propose a more widely applicable definition in this work. This definition has good mathematical properties, and it is based on the definition of a zeta function for complex networks.

scholarly journals Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

2020 ◽  
Vol 117 (26) ◽  
pp. 14812-14818 ◽  
Author(s):  
Bin Zhou ◽  
Xiangyi Meng ◽  
H. Eugene Stanley
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Real World ◽  
Preferential Attachment ◽  
Statistical Tests ◽  
Finite Size ◽  
Distance Distribution ◽  
Scale Free ◽  
Degree Distance

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset,Nat. Commun.10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

VULNERABILITY AND FALL OF EFFICIENCY IN COMPLEX NETWORKS: A NEW APPROACH WITH COMPUTATIONAL ADVANTAGES

2009 ◽  
Vol 19 (02) ◽  
pp. 727-735 ◽  
Author(s):  
S. BOCCALETTI ◽  
R. CRIADO ◽  
J. PELLO ◽  
M. ROMANCE ◽  
M. VELA-PÉREZ
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
New Approach ◽  
And Performance ◽  
Definition Of

An efficient and computationally advantageous definition of vulnerability of a complex network is introduced, through which one is able to overcome a series of practical difficulties encountered by the measurements used so far to quantify a network's security and stability under the effects of failures, attacks or disfunctions. By means of this approach, we prove a series of theorems that allow to gather information on the ranking of the nodes of a network with respect to their strategic importance in order to preserve the functioning and performance of the network as a whole.

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 STRENGTH DISTRIBUTION IN DERIVATIVE NETWORKS

2005 ◽  
Vol 16 (07) ◽  
pp. 1097-1105 ◽  
Author(s):  
LUCIANO DA FONTOURA COSTA ◽  
GONZALO TRAVIESO
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Lower Limit ◽  
Network Model ◽  
Power Law ◽  
Neuronal Networks ◽  
Strength Distribution ◽  
Node Degree ◽  
Upper Limit ◽  
The Difference

This article describes a complex network model whose weights are proportional to the difference between uniformly distributed "fitness" values assigned to the nodes. It is shown both analytically and experimentally that the strength density (i.e., the weighted node degree) for this model, called derivative complex networks, follows a power law with exponent γ<1 if the fitness has an upper limit and γ>1 if the fitness has no upper limit but a positive lower limit. Possible implications for neuronal networks topology and dynamics are also discussed.

scholarly journals Geometrical congruence and efficient greedy navigability of complex networks

2020 ◽  
Author(s):  
Carlo Cannistraci ◽  
Alessandro Muscoloni
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Hyperbolic Space ◽  
Power Law ◽  
Shortest Paths ◽  
Network Measure ◽  
Power Law Exponent ◽  
Current Belief ◽  
Networks Analysis ◽  
Structural Brain

Abstract Hyperbolic networks are supposed to be congruent with their underlying latent geometry and following geodesics in the hyperbolic space is believed equivalent to navigate through topological shortest paths (TSP). This assumption of geometrical congruence is considered the reason for nearly maximally efficient greedy navigation of hyperbolic networks. Here, we propose a complex network measure termed geometrical congruence (GC) and we show that there might exist different TSP, whose projections (pTSP) in the hyperbolic space largely diverge, and significantly differ from the respective geodesics. We discover that, contrary to current belief, hyperbolic networks do not demonstrate in general geometrical congruence and efficient navigability which, in networks generated with nPSO model, seem to emerge only for power-law exponent close to 2. We conclude by showing that GC measure can impact also real networks analysis, indeed it significantly changes in structural brain connectomes grouped by gender or age.

scholarly journals A new structural entropy measurement of networks based on the nonextensive statistical mechanics and hub repulsion

2021 ◽  
Vol 18 (6) ◽  
pp. 9253-9263
Author(s):  
Fu Tan ◽  
◽  
Bing Wang ◽  
Daijun Wei
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Structural Properties ◽  
Complex Network ◽  
Repulsive Force ◽  
Nonextensive Statistical Mechanics ◽  
Entropy Measurement ◽  
Structural Entropy ◽  
Degree Structure ◽  
The Difference

<abstract><p>The structure properties of complex networks are an open issue. As the most important parameter to describe the structural properties of the complex network, the structure entropy has attracted much attention. Recently, the researchers note that hub repulsion plays an role in structural entropy. In this paper, the repulsion between nodes in complex networks is simulated when calculating the structure entropy of the complex network. Coulomb's law is used to quantitatively express the repulsive force between two nodes of the complex network, and a new structural entropy based on the Tsallis nonextensive statistical mechanics is proposed. The new structure entropy synthesizes the influence of repulsive force and betweenness. We study several construction networks and some real complex networks, the results show that the proposed structure entropy can describe the structural properties of complex networks more reasonably. In particular, the new structural entropy has better discrimination in describing the complexity of the irregular network. Because in the irregular network, the difference of the new structure entropy is larger than that of degree structure entropy, betweenness structure entropy and Zhang's structure entropy. It shows that the new method has better discrimination for irregular networks, and experiments on Graph, Centrality literature, US Aire lines and Yeast networks confirm this conclusion.</p></abstract>

Information on evolutionary age in redundancy of complex network

2019 ◽  
Vol 33 (27) ◽  
pp. 1950331
Author(s):  
Shiguo Deng ◽  
Henggang Ren ◽  
Tongfeng Weng ◽  
Changgui Gu ◽  
Huijie Yang
Keyword(s):  
Principal Component Analysis ◽  
Complex Networks ◽  
Metabolic Network ◽  
Complex Network ◽  
Cellular Networks ◽  
Topological Structure ◽  
Quantitative Measure ◽  
Principal Component ◽  
Evolutionary Information ◽  
Local Patterns

Evolutionary processes of many complex networks in reality are dominated by duplication and divergence. This mechanism leads to redundant structures, i.e. some nodes share most of their neighbors and some local patterns are similar, called redundancy of network. An interesting reverse problem is to discover evolutionary information from the present topological structure. We propose a quantitative measure of redundancy of network from the perspective of principal component analysis. The redundancy of a community in the empirical human metabolic network is negatively and closely related with its evolutionary age, which is consistent with that for the communities in the modeling protein–protein network. This behavior can be used to find the evolutionary difference stored in cellular networks.

scholarly journals CNFE-SE: a novel approach combining complex network-based feature engineering and stacked ensemble to predict the success of intrauterine insemination and ranking the features

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Sima Ranjbari ◽  
Toktam Khatibi ◽  
Ahmad Vosough Dizaji ◽  
Hesamoddin Sajadi ◽  
Mehdi Totonchi ◽  
...  
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Semen Quality ◽  
Intrauterine Insemination ◽  
Machine Learning Algorithms ◽  
Semen Parameters ◽  
Feature Engineering ◽  
Operating Characteristics ◽  
Scoring Method ◽  
Novel Approach

Abstract Background Intrauterine Insemination (IUI) outcome prediction is a challenging issue which the assisted reproductive technology (ART) practitioners are dealing with. Predicting the success or failure of IUI based on the couples' features can assist the physicians to make the appropriate decision for suggesting IUI to the couples or not and/or continuing the treatment or not for them. Many previous studies have been focused on predicting the in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) outcome using machine learning algorithms. But, to the best of our knowledge, a few studies have been focused on predicting the outcome of IUI. The main aim of this study is to propose an automatic classification and feature scoring method to predict intrauterine insemination (IUI) outcome and ranking the most significant features. Methods For this purpose, a novel approach combining complex network-based feature engineering and stacked ensemble (CNFE-SE) is proposed. Three complex networks are extracted considering the patients' data similarities. The feature engineering step is performed on the complex networks. The original feature set and/or the features engineered are fed to the proposed stacked ensemble to classify and predict IUI outcome for couples per IUI treatment cycle. Our study is a retrospective study of a 5-year couples' data undergoing IUI. Data is collected from Reproductive Biomedicine Research Center, Royan Institute describing 11,255 IUI treatment cycles for 8,360 couples. Our dataset includes the couples' demographic characteristics, historical data about the patients' diseases, the clinical diagnosis, the treatment plans and the prescribed drugs during the cycles, semen quality, laboratory tests and the clinical pregnancy outcome. Results Experimental results show that the proposed method outperforms the compared methods with Area under receiver operating characteristics curve (AUC) of 0.84 ± 0.01, sensitivity of 0.79 ± 0.01, specificity of 0.91 ± 0.01, and accuracy of 0.85 ± 0.01 for the prediction of IUI outcome. Conclusions The most important predictors for predicting IUI outcome are semen parameters (sperm motility and concentration) as well as female body mass index (BMI).

scholarly journals Connecting complex networks to nonadditive entropies

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. M. de Oliveira ◽  
Samuraí Brito ◽  
L. R. da Silva ◽  
Constantino Tsallis
Keyword(s):  
Statistical Mechanics ◽  
Energy Distribution ◽  
Complex Networks ◽  
Wide Class ◽  
Scale Invariant ◽  
Nonlocal Effects ◽  
Geometric Problem ◽  
Exponential Factor ◽  
Research Areas ◽  
Quasi Stationary State

AbstractBoltzmann–Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving nonlocal space–time entanglement. Its generalization based on nonadditive q-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a d-dimensional geographically located network with weighted links and exhibit its ‘energy’ distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann–Gibbs exponential factor is generically substituted by its q-generalisation, and is recovered in the $$q=1$$ q = 1 limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

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