scholarly journals Degree difference: a simple measure to characterize structural heterogeneity in complex networks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Amirhossein Farzam ◽  
Areejit Samal ◽  
Jürgen Jost
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Degree Sequence ◽  
Structural Heterogeneity ◽  
Local Network ◽  
Basic Unit ◽  
Local Geometry ◽  
Scale Free ◽  
Mixing Patterns ◽  
Topological Robustness

AbstractDespite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, ‘degree difference’ (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and show that DD can reveal structural properties that are not obtained from other such measures in network science. Typically, edges with different DD play different structural roles and the DD distribution is an important network signature. Notably, DD is the basic unit of assortativity. We provide an explanation as to why DD can characterize structural heterogeneity in mixing patterns unlike global assortativity and local node assortativity. By analyzing synthetic and real networks, we show that DD distribution can be used to distinguish between different types of networks including those networks that cannot be easily distinguished using degree sequence and global assortativity. Moreover, we show DD to be an indicator for topological robustness of scale-free networks. Overall, DD is a local measure that is simple to define, easy to evaluate, and that reveals structural properties of networks not readily seen from other measures.

Efficient weighting strategy for enhancing synchronizability of complex networks

2018 ◽  
Vol 32 (11) ◽  
pp. 1850128 ◽  
Author(s):  
Youquan Wang ◽  
Feng Yu ◽  
Shucheng Huang ◽  
Juanjuan Tu ◽  
Yan Chen
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Real World ◽  
Centrality Measures ◽  
Node Degree ◽  
Scale Free ◽  
High Propensity ◽  
Network Link ◽  
Weighting Strategy ◽  
Weighting Methods

Networks with high propensity to synchronization are desired in many applications ranging from biology to engineering. In general, there are two ways to enhance the synchronizability of a network: link rewiring and/or link weighting. In this paper, we propose a new link weighting strategy based on the concept of the neighborhood subgroup. The neighborhood subgroup of a node i through node j in a network, i.e. [Formula: see text], means that node u belongs to [Formula: see text] if node u belongs to the first-order neighbors of j (not include i). Our proposed weighting schema used the local and global structural properties of the networks such as the node degree, betweenness centrality and closeness centrality measures. We applied the method on scale-free and Watts–Strogatz networks of different structural properties and show the good performance of the proposed weighting scheme. Furthermore, as model networks cannot capture all essential features of real-world complex networks, we considered a number of undirected and unweighted real-world networks. To the best of our knowledge, the proposed weighting strategy outperformed the previously published weighting methods by enhancing the synchronizability of these real-world networks.

A Small-World Model of Scale-Free Networks: Features and Verifications

2011 ◽  
Vol 50-51 ◽  
pp. 166-170 ◽  
Author(s):  
Wen Jun Xiao ◽  
Shi Zhong Jiang ◽  
Guan Rong Chen
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Sequence ◽  
Small World ◽  
Static Condition ◽  
Vertex Degree ◽  
Power Law Distribution ◽  
Least Common Multiple ◽  
Scale Free ◽  
Vertex Degrees

It is now well known that many large-sized complex networks obey a scale-free power-law vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent  2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of , , . . ., , and l is less than log N, where l = < is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks.

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.

scholarly journals Network robustness improvement via long-range links

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Vincenza Carchiolo ◽  
Marco Grassia ◽  
Alessandro Longheu ◽  
Michele Malgeri ◽  
Giuseppe Mangioni
Keyword(s):  
Complex Networks ◽  
Long Range ◽  
Real World ◽  
Network Robustness ◽  
Scale Free ◽  
Area Of Interest ◽  
Before And After ◽  
Significant Area ◽  
Better Than

AbstractMany systems are today modelled as complex networks, since this representation has been proven being an effective approach for understanding and controlling many real-world phenomena. A significant area of interest and research is that of networks robustness, which aims to explore to what extent a network keeps working when failures occur in its structure and how disruptions can be avoided. In this paper, we introduce the idea of exploiting long-range links to improve the robustness of Scale-Free (SF) networks. Several experiments are carried out by attacking the networks before and after the addition of links between the farthest nodes, and the results show that this approach effectively improves the SF network correct functionalities better than other commonly used strategies.

scholarly journals Complex networks of earthquakes and aftershocks

2005 ◽  
Vol 12 (1) ◽  
pp. 1-11 ◽  
Author(s):  
M. Baiesi ◽  
M. Paczuski
Keyword(s):  
Complex Networks ◽  
Time Windows ◽  
Scaling Law ◽  
Relative Strength ◽  
Modern Theory ◽  
Significant Information ◽  
Data Set ◽  
Scale Free ◽  
Main Shocks ◽  
Aftershock Sequences

Abstract. We invoke a metric to quantify the correlation between any two earthquakes. This provides a simple and straightforward alternative to using space-time windows to detect aftershock sequences and obviates the need to distinguish main shocks from aftershocks. Directed networks of earthquakes are constructed by placing a link, directed from the past to the future, between pairs of events that are strongly correlated. Each link has a weight giving the relative strength of correlation such that the sum over the incoming links to any node equals unity for aftershocks, or zero if the event had no correlated predecessors. A correlation threshold is set to drastically reduce the size of the data set without losing significant information. Events can be aftershocks of many previous events, and also generate many aftershocks. The probability distribution for the number of incoming and outgoing links are both scale free, and the networks are highly clustered. The Omori law holds for aftershock rates up to a decorrelation time that scales with the magnitude, m, of the initiating shock as tcutoff~10β m with β~-3/4. Another scaling law relates distances between earthquakes and their aftershocks to the magnitude of the initiating shock. Our results are inconsistent with the hypothesis of finite aftershock zones. We also find evidence that seismicity is dominantly triggered by small earthquakes. Our approach, using concepts from the modern theory of complex networks, together with a metric to estimate correlations, opens up new avenues of research, as well as new tools to understand seismicity.

scholarly journals Identifying Node Importance in a Complex Network Based on Node Bridging Feature

2018 ◽  
Vol 8 (10) ◽  
pp. 1914 ◽  
Author(s):  
Lincheng Jiang ◽  
Yumei Jing ◽  
Shengze Hu ◽  
Bin Ge ◽  
Weidong Xiao
Keyword(s):  
Complex Networks ◽  
Large Scale ◽  
Shortest Paths ◽  
Evaluation Criteria ◽  
Local Network ◽  
Network Efficiency ◽  
Network Attack ◽  
Node Importance ◽  
Pass Through ◽  
Large Scale Networks

Identifying node importance in complex networks is of great significance to improve the network damage resistance and robustness. In the era of big data, the size of the network is huge and the network structure tends to change dynamically over time. Due to the high complexity, the algorithm based on the global information of the network is not suitable for the analysis of large-scale networks. Taking into account the bridging feature of nodes in the local network, this paper proposes a simple and efficient ranking algorithm to identify node importance in complex networks. In the algorithm, if there are more numbers of node pairs whose shortest paths pass through the target node and there are less numbers of shortest paths in its neighborhood, the bridging function of the node between its neighborhood nodes is more obvious, and its ranking score is also higher. The algorithm takes only local information of the target nodes, thereby greatly improving the efficiency of the algorithm. Experiments performed on real and synthetic networks show that the proposed algorithm is more effective than benchmark algorithms on the evaluation criteria of the maximum connectivity coefficient and the decline rate of network efficiency, no matter in the static or dynamic attack manner. Especially in the initial stage of attack, the advantage is more obvious, which makes the proposed algorithm applicable in the background of limited network attack cost.

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.

Optimal Nonlinear Pricing in Social Networks Under Asymmetric Network Information

2020 ◽  
Vol 68 (3) ◽  
pp. 818-833
Author(s):  
Yang Zhang ◽  
Ying-Ju Chen
Keyword(s):  
Social Networks ◽  
Nonlinear Pricing ◽  
Local Network ◽  
Solution Approach ◽  
Scale Free ◽  
Network Information ◽  
Pricing Decisions ◽  
Pricing Scheme ◽  
The Social ◽  
Free Network

How should a firm make pricing decisions in social networks when the customers hold in private their local network information? In “Optimal Nonlinear Pricing in Social Networks Under Asymmetric Network Information,” Zhang and Chen develop a solution approach based on calculus of variations and positive neighbor affiliation to tackle this problem. They show that the optimal pricing compromises the capitalization of the susceptibility to neighbor consumption with the motivation of one’s own consumption, which gives rise to a menu of quantity premium or quantity discount. In the Erdös and Rényi graph (a special case of the social network model in this paper), they find that the pricing scheme does not screen network positions; consequently, the firm can offer a simple uniform price. The authors also find that, in the context of two-way connections, the firm-optimal consumption becomes linear in customer degree in the scale-free network.

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