On the Dynamics of Complex Network

2017 ◽  
Author(s):  
Chun-Lin Yang ◽  
C. Steve Suh
Keyword(s):  
Statistical Mechanics ◽  
Complex Network ◽  
Real World ◽  
Local Level ◽  
Structure Model ◽  
Statistical Entropy ◽  
Network Configuration ◽  
Visual Contact ◽  
Network Systems ◽  
Network Property

Controlling complex network systems is challenging because network systems are highly coupled by ensembles and behaving with uncertainty. A network is composed by nodes and edges. Edges serve as the connection between nodes to exchange state information and further achieve state consensus. Through edges, the dynamics of individual nodes at the local level intimately affects the network dynamics at the global level. As a following bird can occasionally lose visual contact with the target bird in a flock at any moment, the edge between two nodes in a real world network systems is not necessarily always intact. Contrary to common sense, these real-world networks are usually perfectly stable even when the edges between the nodes are unstable. This suggests that not only nodes are dynamical, edges are dynamical, too. Since the edges between the nodes are changing dynamically, network configuration is also dynamical. Further, edges need be defined and quantified so that the unstable connection behavior can be properly described. The paper explores the concepts of statistical mechanics and statistical entropy to address the particular need. Statistical mechanics describes the behavior of a mechanical system that has uncertain states. Statistical entropy on the other hand defines the distribution of the microstates by probability. Entropy provides a measure of the level of network integrity. With entropy, one can assign desired dynamics to the network to ensure desired network property. This work aims to construct a complex network structure model based on the edge dynamics. Coupled with node self-dynamic and consensus law, a general dynamical network model can be constructed.

On the Proper Description of Complex Network Dynamics

2018 ◽  
Author(s):  
Chun-Lin Yang ◽  
C. Steve Suh
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Collective Behavior ◽  
Local Level ◽  
Network Dynamics ◽  
Global Dynamics ◽  
Statistical Entropy ◽  
Network Systems ◽  
Local Dynamics ◽  
The Difference

Real-world networks are dynamical complex network systems. The dynamics of a network system is a coupling of the local dynamics with the global dynamics. The local dynamics is the time-varying behaviors of ensembles at the local level. The global dynamics is the collective behavior of the ensembles following specific laws at the global level. These laws include basic physical principles and constraints. Complex networks have inherent resilience that offsets disturbance and maintains the state of the system. However, when disturbance is potent enough, network dynamics can be perturbed to a level that ensembles no longer follow the constraint conditions. As a result, the collective behavior of a complex network diminishes and the network collapses. The characteristic of a complex network is the response of the system which is time-dependent. Therefore, complex networks need to account for time-dependency and obey physical laws and constraints. Statistical mechanics is viable for the study of multi-body dynamic systems having uncertain states such as complex network systems. Statistical entropy can be used to define the distribution of the states of ensembles. The difference between the states of ensembles define the interaction between them. This interaction is known as the collective behavior. In other words statistical entropy defines the dynamics of a complex network. Variation of entropy corresponds to the variation of network dynamics and vice versa. Therefore, entropy can serve as an indicator of network dynamics. A stable network is characterized by a specific entropy while a network on the verge of collapse is characterized by another. As the collective behavior of a complex network can be described by entropy, the correlation between the statistical entropy and network dynamics is investigated.

scholarly journals Ripple-Spreading Network Model Optimization by Genetic Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xiao-Bing Hu ◽  
Ming Wang ◽  
Mark S. Leeson
Keyword(s):  
Genetic Algorithm ◽  
Complex Network ◽  
Network Model ◽  
Real World ◽  
Network Models ◽  
Small World ◽  
Network Systems ◽  
Scale Free ◽  
Apply Genetic ◽  
Network Topologies

Small-world and scale-free properties are widely acknowledged in many real-world complex network systems, and many network models have been developed to capture these network properties. The ripple-spreading network model (RSNM) is a newly reported complex network model, which is inspired by the natural ripple-spreading phenomenon on clam water surface. The RSNM exhibits good potential for describing both spatial and temporal features in the development of many real-world networks where the influence of a few local events spreads out through nodes and then largely determines the final network topology. However, the relationships between ripple-spreading related parameters (RSRPs) of RSNM and small-world and scale-free topologies are not as obvious or straightforward as in many other network models. This paper attempts to apply genetic algorithm (GA) to tune the values of RSRPs, so that the RSNM may generate these two most important network topologies. The study demonstrates that, once RSRPs are properly tuned by GA, the RSNM is capable of generating both network topologies and therefore has a great flexibility to study many real-world complex network systems.

Effects of link perturbation on network modularity for community detections in complex network systems

2021 ◽  
pp. 2150214
Author(s):  
Dongyan Zhao ◽  
Jing Li ◽  
Zhongyuan Jiang
Keyword(s):  
Complex Network ◽  
Community Detection ◽  
Real World ◽  
Perturbation Methods ◽  
Random Perturbation ◽  
Network Structures ◽  
Network Systems ◽  
Network Modularity ◽  
The Impact

Community detection is of great significance in analyzing the network structures. However, real networks usually contain missing links and spurious interactions, which affect the accuracy of community detection results. In this paper, we aim to find out the regularity of the impact on community detection when links are deleted from or added to the network. To address this problem, we propose degree-related link perturbation (DRLP) methods for the tasks of both deleting and adding links, and the random perturbation methods are also be employed. Then, we evaluate the impact of perturbation methods on community detection and draw some conclusions. Finally, extensive experiments conducted on six real-world networks demonstrate the existence of the regularity. The perturbation of deleting and adding links can lead to continuous rise and decline of modularity, respectively, which is also instructive to change the results of community detection purposefully.

scholarly journals Asymmetry underlies stability in power grids

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ferenc Molnar ◽  
Takashi Nishikawa ◽  
Adilson E. Motter
Keyword(s):  
Symmetry Breaking ◽  
Real World ◽  
Power Grids ◽  
Stable Operation ◽  
World Systems ◽  
Symmetric State ◽  
Network Systems ◽  
Additional Improvement ◽  
The Stability ◽  
General Method

AbstractBehavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.

How can historical knowledge help us to make sense of communities like Rotherham?

2018 ◽  
Author(s):  
Elizabeth Pente ◽  
Paul Ward
Keyword(s):  
Real World ◽  
Local Level ◽  
Historical Knowledge ◽  
Everyday Lives

This chapter addresses the question of how historical knowledge can help one to make sense of communities like Rotherham. It first considers what counts as ‘historical knowledge’, and examines the limitations of historiography in producing histories at a local level, where issues of class, gender, and ethnicity are played out in people's everyday lives. The chapter then explores how historians are expanding what counts for historical knowledge — in particular, the co-production of research, which can be defined as research with people rather than on people. It also provides some real-world examples of co-production in action. Finally, the chapter provides some arguments as to why historical knowledge matters.

scholarly journals Dividend Policy, Personal Taxes and Optimal Capital Structure

2020 ◽  
Vol 9 (2) ◽  
pp. 1
Author(s):  
Sheen Liu ◽  
Yan Alice Xie
Keyword(s):  
Capital Structure ◽  
Real World ◽  
Dividend Policy ◽  
Credit Spreads ◽  
Structure Model ◽  
Optimal Capital Structure ◽  
Personal Taxes ◽  
Wide Range ◽  
Optimal Capital ◽  
Tax Benefits

<p>This paper puts forward a capital structure model that incorporates the impacts of dividend policy and personal taxes that are commonly ignored by the existing capital structure models. The results show that paying dividends can reduce the tax benefits from issuing debts, which explains why existing capital structure models commonly overestimate leverage ratios. The results further show that as dividend payout increases, leverage ratios and credit spreads increase too. By incorporating the impacts of dividend policy and personal taxes, the capital structure model established in this paper can generate wide range of leverage ratios and credit spreads, which are consistent with what are observed in the real world.</p>

Analyses of the response of a complex weighted network to nodes removal strategies considering links weight: The case of the Beijing urban road system

2018 ◽  
Vol 32 (05) ◽  
pp. 1850067 ◽  
Author(s):  
Michele Bellingeri ◽  
Zhe-Ming Lu ◽  
Davide Cassi ◽  
Francesco Scotognella
Keyword(s):  
Complex Network ◽  
Real World ◽  
Road Traffic ◽  
Network Efficiency ◽  
Weighted Network ◽  
Node Importance ◽  
Connected Cluster ◽  
Binary Network ◽  
Binary Networks ◽  
Weighted Rank

Complex network response to node loss is a central question in different fields of science ranging from physics, sociology, biology to ecology. Previous studies considered binary networks where the weight of the links is not accounted for. However, in real-world networks the weights of connections can be widely different. Here, we analyzed the response of real-world road traffic complex network of Beijing, the most prosperous city in China. We produced nodes removal attack simulations using classic binary node features and we introduced weighted ranks for node importance. We measured the network functioning during nodes removal with three different parameters: the size of the largest connected cluster (LCC), the binary network efficiency (Bin EFF) and the weighted network efficiency (Weg EFF). We find that removing nodes according to weighted rank, i.e. considering the weight of the links as a number of taxi flows along the roads, produced in general the highest damage in the system. Our results show that: (i) in order to model Beijing road complex networks response to nodes (intersections) failure, it is necessary to consider the weight of the links; (ii) to discover the best attack strategy, it is important to use nodes rank accounting links weight.

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.

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