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>

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.

Improved efficient routing strategy on two-layer complex networks

2016 ◽  
Vol 27 (04) ◽  
pp. 1650044 ◽  
Author(s):  
Jinlong Ma ◽  
Weizhan Han ◽  
Qing Guo ◽  
Shuai Zhang ◽  
Junfang Wang ◽  
...  
Keyword(s):  
Complex Networks ◽  
Research Topic ◽  
Global Awareness ◽  
Traffic Dynamics ◽  
Shortest Path Routing ◽  
Transport Efficiency ◽  
Routing Strategy ◽  
Traffic Capacity ◽  
Traffic Performance ◽  
Simulation Results

The traffic dynamics of multi-layer networks has become a hot research topic since many networks are comprised of two or more layers of subnetworks. Due to its low traffic capacity, the traditional shortest path routing (SPR) protocol is susceptible to congestion on two-layer complex networks. In this paper, we propose an efficient routing strategy named improved global awareness routing (IGAR) strategy which is based on the betweenness centrality of nodes in the two layers. With the proposed strategy, the routing paths can bypass hub nodes of both layers to enhance the transport efficiency. Simulation results show that the IGAR strategy can bring much better traffic capacity than the SPR and the global awareness routing (GAR) strategies. Because of the significantly improved traffic performance, this study is helpful to alleviate congestion of the two-layer complex networks.

scholarly journals Graph fractal dimension and the structure of fractal networks

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Pavel Skums ◽  
Leonid Bunimovich
Keyword(s):  
Complex Networks ◽  
Evolutionary Biology ◽  
Real Life ◽  
Fractal Dimensions ◽  
Network Models ◽  
Self Similarity ◽  
Descriptive Complexity ◽  
Network Communities ◽  
Fractal Properties ◽  
Continuous Objects

Abstract Fractals are geometric objects that are self-similar at different scales and whose geometric dimensions differ from so-called fractal dimensions. Fractals describe complex continuous structures in nature. Although indications of self-similarity and fractality of complex networks has been previously observed, it is challenging to adapt the machinery from the theory of fractality of continuous objects to discrete objects such as networks. In this article, we identify and study fractal networks using the innate methods of graph theory and combinatorics. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to known graph-theoretical characteristics: rank dimension and product dimension. Our approach reveals how self-similarity and fractality of a network are defined by a pattern of overlaps between densely connected network communities. It allows us to identify fractal graphs, explore the relations between graph fractality, graph colourings and graph descriptive complexity, and analyse the fractality of several classes of graphs and network models, as well as of a number of real-life networks. We demonstrate the application of our framework in evolutionary biology and virology by analysing networks of viral strains sampled at different stages of evolution inside their hosts. Our methodology revealed gradual self-organization of intra-host viral populations over the course of infection and their adaptation to the host environment. The obtained results lay a foundation for studying fractal properties of complex networks using combinatorial methods and algorithms.

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.

Link Scheduling Scheme for Multi-Hop Cognitive Radio Ad Hoc Networks

2013 ◽  
Vol 443 ◽  
pp. 430-434
Author(s):  
Chao Li ◽  
Guo Chun Ren ◽  
Cheng Gui Wang ◽  
Yu Bo Wang
Keyword(s):  
Ad Hoc ◽  
Scheduling Algorithm ◽  
Cluster Head ◽  
Link Scheduling ◽  
Destination Node ◽  
Spatial Reuse ◽  
Topology Structure ◽  
Scheduling Scheme ◽  
Simulation Results ◽  
Hoc Networks

In this paper, we propose to apply a centre scheduling algorithm in the CRAHNs with a cluster. In this network, the cluster head assigns time slots to each node so that every node can be fair to transfer data. The scheme schedules the links to the same destination node first, which has the largest topology structure, then another destination node whose topology structure is larger than the rest. The algorithm presented in this paper considers both the fairness and the spatial reuse, and the simulation results show that this algorithm still has a good performance when the topology is so large.

scholarly journals Controllability and Optimization of Complex Networks Based on Bridges

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lifu Wang ◽  
Guotao Zhao ◽  
Zhi Kong ◽  
Yunkang Zhao
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Betweenness Centrality ◽  
The Other ◽  
Connected Components ◽  
Scale Free ◽  
Scale Free Networks ◽  
Model Networks ◽  
Simulation Results ◽  
And Control

In a complex network, each edge has different functions on controllability of the whole network. A network may be out of control due to failure or attack of some specific edges. Bridges are a kind of key edges whose removal will disconnect a network and increase connected components. Here, we investigate the effects of removing bridges on controllability of network. Various strategies, including random deletion of edges, deletion based on betweenness centrality, and deletion based on degree of source or target nodes, are used to compare with the effect of removing bridges. It is found that the removing bridges strategy is more efficient on reducing controllability than the other strategies of removing edges for ER networks and scale-free networks. In addition, we also found the controllability robustness under edge attack is related to the average degree of complex networks. Therefore, we propose two optimization strategies based on bridges to improve the controllability robustness of complex networks against attacks. The effectiveness of the proposed strategies is demonstrated by simulation results of some model networks. These results are helpful for people to understand and control spreading processes of epidemic across different paths.

Design of Structural Controllability for Complex Network Architecture

2016 ◽  
pp. 98-124
Author(s):  
Amitava Mukherjee ◽  
Ayan Chatterjee ◽  
Debayan Das ◽  
Mrinal K. Naskar
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Network Architecture ◽  
Structural Control ◽  
Link Failures ◽  
Novel Approach ◽  
Minimum Number ◽  
Structural Controllability ◽  
Reduced Complexity ◽  
Simulation Results

Networks are all-pervasive in nature. The complete structural controllability of a network and its robustness against unwanted link failures and perturbations are issues of immense concern. In this chapter, we propose a heuristic to determine the minimum number of driver nodes for complete structural control, with a reduced complexity. We also introduce a novel approach to address the vulnerability of the real-world complex networks, and enhance the robustness of the network, prior to an attack or failure. The simulation results reveal that dense and homogenous networks are easier to control with lesser driver nodes, and are more robust, compared to sparse and inhomogeneous networks.

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