Universal Dynamics on Complex Networks, Really?

2011 ◽  
pp. 231-249
Author(s):  
Brigitte Gay
Keyword(s):  
Complex Networks ◽  
Statistical Physics ◽  
Small World ◽  
Theoretical Understanding ◽  
Scale Free ◽  
Scale Free Networks ◽  
Universal Properties ◽  
Universal Structure ◽  
Using Data ◽  
Empirical Networks

The complex network approach developed in statistical physics seems particularly well-suited to analyzing large networks. Progress in the study of complex networks has been made by looking for shared properties and seemingly universal dynamics, thus ignoring the details of networks individual nodes, links, or sub-components. Researchers now need to assess the differences in the processes that take place on complex networks. The author first discusses briefly the theoretical understanding of evolutionary laws governing the emergence of these universal properties (small-world and scale-free networks) and recent evolutions in the field of network analysis. Using data on two empirical networks, a transaction network in the venture capital industry and an interfirm alliance network in a major sector of the biopharmaceutical industry, the author then demonstrates that networks can switch from one ‘universal’ structure to another, but each in its own way. This chapter highlights the need of knowing more about networks, as ‘more is different’.

Propagation and stability in software: A complex network perspective

2015 ◽  
Vol 26 (05) ◽  
pp. 1550052 ◽  
Author(s):  
Lei Wang ◽  
Ping Wang
Keyword(s):  
Software Engineering ◽  
Complex Networks ◽  
Large Scale ◽  
Structural Difference ◽  
Small World ◽  
Change Propagation ◽  
Small World Networks ◽  
Typical Structure ◽  
Scale Free ◽  
Scale Free Networks

In this paper, we attempt to understand the propagation and stability feature of large-scale complex software from the perspective of complex networks. Specifically, we introduced the concept of "propagation scope" to investigate the problem of change propagation in complex software. Although many complex software networks exhibit clear "small-world" and "scale-free" features, we found that the propagation scope of complex software networks is much lower than that of small-world networks and scale-free networks. Furthermore, because the design of complex software always obeys the principles of software engineering, we introduced the concept of "edge instability" to quantify the structural difference among complex software networks, small-world networks and scale-free networks. We discovered that the edge instability distribution of complex software networks is different from that of small-world networks and scale-free networks. We also found a typical structure that contributes to the edge instability distribution of complex software networks. Finally, we uncovered the correlation between propagation scope and edge instability in complex networks by eliminating the edges with different instability ranges.

Complex networks

2018 ◽  
Author(s):  
Graziano Vernizzi ◽  
Henri Orland
Keyword(s):  
Complex Networks ◽  
Small World ◽  
Laplacian Matrix ◽  
Square Lattice ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Scale Free Graphs ◽  
Regular Networks

This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.

Research on Edge-Growing Models Related with Scale-Free Small-World Networks

2014 ◽  
Vol 513-517 ◽  
pp. 2444-2448 ◽  
Author(s):  
Bing Yao ◽  
Ming Yao ◽  
Xiang En Chen ◽  
Xia Liu ◽  
Wan Jia Zhang
Keyword(s):  
Complex Networks ◽  
Topological Structure ◽  
Spanning Trees ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Growing Network

Understanding the topological structure of scale-free networks or small world networks is required and useful for investigation of complex networks. We will build up a class of edge-growing network models and provide an algorithm for finding spanning trees of edge-growing network models in this article.

TOWARD A HARMONIOUS UNIFYING HYBRID MODEL FOR ANY EVOLVING COMPLEX NETWORKS

2007 ◽  
Vol 10 (02) ◽  
pp. 117-141 ◽  
Author(s):  
JINQING FANG ◽  
QIAO BI ◽  
YONG LI ◽  
XIN-BIAO LU ◽  
QIANG LIU
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Small World ◽  
Current Interest ◽  
Topological Properties ◽  
Small World Networks ◽  
Scale Free ◽  
Evolving Networks ◽  
Scale Free Networks ◽  
Hybrid Mechanisms

The current interest in complex networks is a part of a broader movement towards research on complex systems. Motivation of this work raises the two challenging questions: (i) Are real networks fundamentally random preferential attached without any deterministic attachment for both un-weighted and weighted networks? (ii) Is there a coherent physical idea and model for unifying the study of the formation mechanism of complex networks? To answer these questions, we propose a harmonious unifying hybrid preferential model (HUHPM) to a certain class of complex networks, which is controlled by a hybrid ratio, d/r, and study their behavior both numerically and analytically. As typical examples, we apply the concepts and method of the HUHPM to un-weighted scale-free networks proposed by Barabasi and Albert (BA), weighted evolving networks proposed by Barras, Bartholomew and Vespignani (BBV), and the traffic driven evolution (TDE) networks proposed by Wang et al., to get the so-called HUHPM-BA, HUHPM-BBV and HUHPM-TDE networks. All the findings of topological properties in the above three typical HUHPM networks give certain universal meaningful results which reveal some essential hybrid mechanisms for the formation of nontrivial scale-free and small-world networks.

Robustness of complex networks with both unidirectional and bidirectional links against cascading failures

2017 ◽  
Vol 31 (27) ◽  
pp. 1750252 ◽  
Author(s):  
Lin Ding ◽  
Victor C. M. Leung ◽  
Min-Sheng Tan
Keyword(s):  
Complex Networks ◽  
Low Cost ◽  
Small World ◽  
Network Robustness ◽  
Cascading Failures ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Simulation Results ◽  
Direction Determining

The robustness of complex networks against cascading failures has been of great interest, while most of the researchers have considered undirected networks. However, to be more realistic, a part of links of many real systems should be described as unidirectional. In this paper, by applying three link direction-determining (DD) strategies, the tolerance of cascading failures is investigated in various networks with both unidirectional and bidirectional links. By extending the utilization of a classical global betweenness method, we propose a new cascading model, taking into account the weights of nodes and the directions of links. Then, the effects of unidirectional links on the network robustness against cascaded attacks are examined under the global load-based distribution mechanism. The simulation results show that the link-directed methods could not always lead to the decrease of the network robustness as indicated in the previous studies. For small-world networks, these methods certainly make the network weaker. However, for scale-free networks, the network robustness can be significantly improved by the link-directed method, especially for the method with non-random DD strategies. These results are independent of the weight parameter of the nodes. Due to the strongly improved robustness and easy realization with low cost on networks, the method for enforcing proper links to the unidirectional ones may be useful for leading to insights into the control of cascading failures in real-world networks, like communication and transportation networks.

scholarly journals On the Distributions of Subgraph Centralities in Complex Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Faxu Li ◽  
Liang Wei ◽  
Haixing Zhao ◽  
Feng Hu
Keyword(s):  
Complex Networks ◽  
Probability Distributions ◽  
Network Connectivity ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Power Law Distribution ◽  
Scale Free ◽  
Scale Free Networks ◽  
Complex Network Models

Subgraph centrality measure characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than large ones, which makes this measure appropriate for characterizing network motifs. This measure is better in being able to discriminate the nodes of a network than alternate measures. In this paper, the important issue of subgraph centrality distributions is investigated through theory-guided extensive numerical simulations, for three typical complex network models, namely, the ER random-graph networks, WS small-world networks, and BA scale-free networks. It is found that these three very different types of complex networks share some common features, particularly that the subgraph centrality distributions in increasing order are all insensitive to the network connectivity characteristics, and also found that the probability distributions of subgraph centrality of the ER and of the WS models both follow the gamma distribution, and the BA scale-free networks exhibit a power-law distribution with an exponential cutoff.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

scholarly journals A Novel Edge Rewire Mechanism Based on Multiobjective Optimization for Network Robustness Enhancement

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhaoxing Li ◽  
Qionghai Liu ◽  
Li Chen
Keyword(s):  
Multiobjective Optimization ◽  
Complex Networks ◽  
Optimization Algorithm ◽  
Real World ◽  
Network Robustness ◽  
Objective Functions ◽  
Swarm Optimization ◽  
Scale Free ◽  
Scale Free Networks ◽  
The Given

A complex network can crash down due to disturbances which significantly reduce the network’s robustness. It is of great significance to study on how to improve the robustness of complex networks. In the literature, the network rewire mechanism is one of the most widely adopted methods to improve the robustness of a given network. Existing network rewire mechanism improves the robustness of a given network by re-connecting its nodes but keeping the total number of edges or by adding more edges to the given network. In this work we propose a novel yet efficient network rewire mechanism which is based on multiobjective optimization. The proposed rewire mechanism simultaneously optimizes two objective functions, i.e., maximizing network robustness and minimizing edge rewire operations. We further develop a multiobjective discrete partite swarm optimization algorithm to solve the proposed mechanism. Compared to existing network rewire mechanisms, the developed mechanism has two advantages. First, the proposed mechanism does not require specific constraints on the rewire mechanism to the studied network, which makes it more feasible for applications. Second, the proposed mechanism can suggest a set of network rewire choices each of which can improve the robustness of a given network, which makes it be more helpful for decision makings. To validate the effectiveness of the proposed mechanism, we carry out experiments on computer-generated Erdős–Rényi and scale-free networks, as well as real-world complex networks. The results demonstrate that for each tested network, the proposed multiobjective optimization based edge rewire mechanism can recommend a set of edge rewire solutions to improve its robustness.

scholarly journals Optimal shattering of complex networks

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Nicole Balashov ◽  
Reuven Cohen ◽  
Avieli Haber ◽  
Michael Krivelevich ◽  
Simi Haber
Keyword(s):  
Complex Networks ◽  
Random Graphs ◽  
Polynomial Time ◽  
Optimal Performance ◽  
Regular Graphs ◽  
Scale Free ◽  
Scale Free Networks ◽  
Minimum Number

Abstract We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size.We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality.Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

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