Bipartite subgraphs and the signless Laplacian matrix

For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalized Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs. Our results are applied to some graphs with degree sequences approximately following a power law distribution with exponent value 2:1 (scale-free networks), and to a scale-free network arising from protein-protein interaction.

Download Full-text

Scale-Free Networks Based on the Value of Interest

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.753-755.2959 ◽

2013 ◽

Vol 753-755 ◽

pp. 2959-2962

Author(s):

Jun Tao Yang ◽

Hui Wen Deng

Keyword(s):

Network Model ◽

Power Law ◽

Scale Free Network ◽

Power Law Distribution ◽

Scale Free ◽

Distribution Property ◽

Scale Free Networks ◽

Free Model ◽

Free Network ◽

Interest Model

Assigning the value of interest to each node in the network, we give a scale-free network model. The value of interest is related to the fitness and the degree of the node. Experimental results show that the interest model not only has the characteristics of the BA scale-free model but also has the characteristics of fitness model, and the network has a power-law distribution property.

Download Full-text

An Abnormal IP Traffic Detection Model Based on Scale-Free Network

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.44-47.849 ◽

2010 ◽

Vol 44-47 ◽

pp. 849-853

Author(s):

Jun Li ◽

Yan Niu

Keyword(s):

Detection System ◽

Anomalous Behavior ◽

Power Exponent ◽

Scale Free Network ◽

Power Law Distribution ◽

Scale Free ◽

Detection Model ◽

Free Network ◽

Traffic Detection ◽

Entire Network

A model of detecting an abnormal IP traffic in a subset of network is described. The model is based on the hypothesis that random sampling subnet are the same probability distribution as the entire network if some conditions are met with, nodes’s degree in IP traffic can be processed as a power-law distribution in scale-free network . The model analyzes the power exponent and relations between the anomalous behavior and parameter r. Finally, a test was conducted by the data, some type attacks could be identified exactly. the model provides a new framework for intrusion-detection system.

Download Full-text

COMPLEX NETWORK SIMULATION OF FOREST NETWORK SPATIAL PATTERN IN PEARL RIVER DELTA

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-2-w7-1445-2017 ◽

2017 ◽

Vol XLII-2/W7 ◽

pp. 1445-1449

Author(s):

Y. Zeng

Keyword(s):

Power Law ◽

Pearl River Delta ◽

Pearl River ◽

Network Node ◽

Scale Free Network ◽

Power Law Distribution ◽

Network Nodes ◽

Scale Free ◽

Node Distribution ◽

Free Network

Forest network-construction uses for the method and model with the scale-free features of complex network theory based on random graph theory and dynamic network nodes which show a power-law distribution phenomenon. The model is suitable for ecological disturbance by larger ecological landscape Pearl River Delta consistent recovery. Remote sensing and GIS spatial data are available through the latest forest patches. A standard scale-free network node distribution model calculates the area of forest network’s power-law distribution parameter value size; The recent existing forest polygons which are defined as nodes can compute the network nodes decaying index value of the network’s degree distribution. The parameters of forest network are picked up then make a spatial transition to GIS real world models. Hence the connection is automatically generated by minimizing the ecological corridor by the least cost rule between the near nodes. Based on scale-free network node distribution requirements, select the number compared with less, a huge point of aggregation as a future forest planning network’s main node, and put them with the existing node sequence comparison. By this theory, the forest ecological projects in the past avoid being fragmented, scattered disorderly phenomena. The previous regular forest networks can be reduced the required forest planting costs by this method. For ecological restoration of tropical and subtropical in south China areas, it will provide an effective method for the forest entering city project guidance and demonstration with other ecological networks (water, climate network, etc.) for networking a standard and base datum.

Download Full-text

Eigenvalue-based entropy in directed complex networks

PLoS ONE ◽

10.1371/journal.pone.0251993 ◽

2021 ◽

Vol 16 (6) ◽

pp. e0251993

Author(s):

Yan Sun ◽

Haixing Zhao ◽

Jing Liang ◽

Xiujuan Ma

Keyword(s):

Complex Networks ◽

Complex Network ◽

Network Models ◽

Small World ◽

Laplacian Matrix ◽

Directed Network ◽

Small World Network ◽

Scale Free Network ◽

Scale Free ◽

Free Network

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

Download Full-text

Evolution of Cooperation through Power Law Distributed Conflicts

Complexity ◽

10.1155/2017/9271651 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7

Author(s):

Pilwon Kim

Keyword(s):

Power Law ◽

Evolution Of Cooperation ◽

Scale Free Network ◽

Power Law Distribution ◽

Homogeneous Population ◽

Interpersonal Conflicts ◽

Personal Resource ◽

Scale Free ◽

Individual Level ◽

Free Network

At an individual level, cooperation can be seen as a behaviour that uses personal resource to support others or the groups which one belongs to. In a conflict between two individuals, a selfish person gains an advantage over a cooperative opponent, while in a group-group conflict the group with more cooperators wins. In this work, we develop a population model with continual conflicts at various scales and show cooperation can be sustained even when interpersonal conflicts dominate, as long as the conflict size follows a power law. The power law assumption has been met in several observations from real-world conflicts. Specifically if the population is structured on a scale-free network, both the power law distribution of conflicts and the survival of cooperation can be naturally induced without assuming a homogeneous population or frequent relocation of members. On the scale-free network, even when most people become selfish from continual person-person conflicts, people on the hubs tend to remain unselfish and play a role as “repositories” of cooperation.

Download Full-text

Applications of Laplacian spectrum for the weighted scale-free network with a weight factor

International Journal of Modern Physics B ◽

10.1142/s0217979218503538 ◽

2018 ◽

Vol 32 (32) ◽

pp. 1850353 ◽

Cited By ~ 2

Author(s):

Meifeng Dai ◽

Tingting Ju ◽

Jingyi Liu ◽

Yu Sun ◽

Xiangmei Song ◽

...

Keyword(s):

Laplacian Matrix ◽

Weight Matrix ◽

Weight Factor ◽

Scale Free Network ◽

Laplacian Spectrum ◽

Kirchhoff Index ◽

Scale Free ◽

Free Network ◽

Eigenvalue And Eigenvector ◽

Binary Scale

Laplacian spectrum gives a lot of useful information about complex structural properties and relevant dynamical aspects, which has attracted the attention of mathematicians. We introduced the weighted scale-free network inspired by the binary scale-free network. First, the weighted scale-free network with a weight factor is constructed by an iterative way. In the next step, we use the definition of eigenvalue and eigenvector to obtain the recursive relationship of its eigenvalues and multiplicities at two successive generations. Through analysis of eigenvalues of transition weight matrix we find that multiplicities of eigenvalues 0 of transition matrix are different for the binary scale-free network and the weighted scale-free network. Then, we obtain the eigenvalues for the normalized Laplacian matrix of the weighted scale-free network by using the obtained eigenvalues of transition weight matrix. Finally, we show some applications of the Laplacian spectrum in calculating eigentime identity and Kirchhoff index. The leading term of these indexes are completely different for the binary and the weighted scale-free network.

Download Full-text

ENHANCING THE SYNCHRONIZABILITY OF SCALE-FREE NETWORKS BY ADDING EDGES

International Journal of Modern Physics C ◽

10.1142/s0129183110014951 ◽

2010 ◽

Vol 21 (01) ◽

pp. 67-77 ◽

Cited By ~ 3

Author(s):

SHENG-JUN WANG ◽

ZHI-XI WU ◽

HAI-RONG DONG ◽

GUANRONG CHEN

Keyword(s):

Nearest Neighbors ◽

Laplacian Matrix ◽

New Method ◽

Scale Free Network ◽

Largest Eigenvalue ◽

Scale Free ◽

Scale Free Networks ◽

Free Network ◽

The Largest Eigenvalue

To efficiently enhance the synchronizability of a scale-free network by adding some edges, we numerically study the effect of edge-adding on the spectrum of the network Laplacian matrix. Based on the relation between the largest eigenvalue of the Laplacian matrix and the largest degree of the scale-free network, we show that adding a new edge to the node of largest degree will generally weaken the synchronizability of a scale-free network. We consequently propose a method to effectively enhance the network synchronizability by attaching the new edge to a node whose nearest-neighbors have small degrees. The effect of the new method is analyzed and demonstrated with comparisons.

Download Full-text

Mathematics and statistics related studies in Indonesia using co-authorship network analysis

International Journal of Advances in Intelligent Informatics ◽

10.26555/ijain.v4i2.120 ◽

2018 ◽

Vol 4 (2) ◽

pp. 142

Author(s):

Irene Muflikh Nadhiroh ◽

Ria Hardiyati ◽

Mia Amelia ◽

Tri Handayani

Keyword(s):

Network Analysis ◽

Web Of Science ◽

Collaboration Network ◽

Scale Free Network ◽

Power Law Distribution ◽

Scale Free ◽

Free Network ◽

Institute Of Technology ◽

Bibliometrics Analysis ◽

Number Of Authors

Indonesian scholars have published a numbers of articles in numerous international publications, however, it still lags behind other Singapore, Malaysia, and Vietnam. This article performs a bibliometrics analysis and examine the collaboration network in Mathematics and Statistics related subject of scholars with Indonesian affiliation as recorded in Web of Science. In total, based on article publications during 2009-2017, 426 articles were retrieved. Bandung Institute of Technology (ITB) was the affiliation with the highest number of articles (48%) and number of authors (27%). Using Social Network Analysis to examine co-authorship networks, this research shows that the co-author network has the highest centrality in the ITB affiliation. Meanwhile, dependency of foreign affiliation is still high, shown as a high percentage (84% of all articles) of international co-authorship. Co-authorship network of Mathematics and Statistics related studies in Indonesia possesses as a scale-free network and followed the power law distribution. This research showed the achievement of Indonesian scholars of Mathematics and Statistics, and can be used to evaluate the knowledge transfer in these subjects and related areas.

Download Full-text