Modelling of a WDM Network Using Graph Theory and Dijkstra Algorithm for Traffic Redirection

Optical transport networks are now the basic infrastructure of modern communications systems, including the SDH and WDM backbone network of local network operators, in the case of Cameroon. Given the colossal investments required to deploy these networks, particularly related to the cost of equipment (optical fibers, transponders and multiplexers), the optimization of bandwidth and dynamic allocation of resources is essential to control operating costs and ensure continuity of service. Automatic switching technology for optical networks brings intelligence to the control plane to fully facilitate bandwidth utilization, traffic redirection, and automatic configuration of end-to-end services. This paper considers a local network operator’s WDM network without the implementation of the automatic switching technology, develops a network modeling software platform called Graphic Networks and using graph theory integrates a particularity of the automatic switching technology, which is the automatic rerouting of traffic in case of incident in the network. The incidents considered here are those links or route failures and node failures.

Regional differences in gully network connectivity based on graph theory:a case study on the Loess Plateau,China

Material exchange frequently occurs in gullies,and thus the relationship between a gullynetwork structure and sediment transport potential has attracted considerable interest.However,previous researches ignored the difficulty of material transport from sources to sinks,and did not quantify the connectivity of a network structure.In this study,we used a graph model structure to model gully networks of six typical sample areas in the Loess Plateau of China and quantified gully network connectivity using four indexes:average node strength,accessibility from sources to sinks,potential flow,and network structural connectivity index.Results show that:(1)Reflected by different quantitative indexes,the trends of gully network connectivity in different regions are similar.From north to south,the connectivity of a sample area first increases and then decreases.(2)The more mature gullies have stronger network connectivity.Small resistance is conducive to material transport in the gullies.(3)The node connectivity index of the gully network shows a significant aggregation distribution in space,and node connectivity on the main channel is often stronger than that on the branch trench.These results not only deepen the understanding of the process and mechanism of loess gully geomorphic development and evolution but also provide a reference for geomorphic studies.

Identifying multiple influential spreaders in complex networks based on spectral graph theory

One of the hot research topics in propagation dynamics is identifying a set of critical nodes that can influence maximization in a complex network.The importance and dispersion of critical nodes among them are both vital factors that can influence maximization.We therefore propose a multiple influential spreaders identification algorithm based on spectral graph theory.This algorithm first quantifies the role played by the local structure of nodes in the propagation process,then classifies the nodes based on the eigenvectors of the Laplace matrix,and finally selects a set of critical nodes by the constraint that nodes in the same class are not adjacent to each other while different classes of nodes can be adjacent to each other.Experimental results on real and synthetic networks show that our algorithm outperforms the state-of-the-art and classical algorithms in the SIR model.

A Graph Theory Based Self-Learning Honeypot to Detect Persistent Threats

Attacks on the cyber space is getting exponential in recent times.Illegal penetrations and breaches are real threats to the individuals and organizations.Conventional security systems are good enough to detect the known threats but when it comes to Advanced Persistent Threats(APTs)they fails.These APTs are targeted,more sophisticated and very persistent and incorporates lot of evasive techniques to bypass the existing defenses.Hence,there is a need for an effective defense system that can achieve a complete reliance of security.To address the above-mentioned issues,this paper proposes a novel honeypot system that tracks the anonymous behavior of the APT threats.The key idea of honeypot leverages the concepts of graph theory to detect such targeted attacks.The proposed honey-pot is self-realizing,strategic assisted which withholds the APTs actionable tech-niques and observes the behavior for analysis and modelling.The proposed graph theory based self learning honeypot using the resultsγ(C(n,1)),γc(C(n,1)),γsc(C(n,1))outperforms traditional techniques by detecting APTs behavioral with detection rate of 96%.

Multi-Body Dynamics Modeling and Simulation Analysis of a Vehicle Suspension Based on Graph Theory

Multi-body dynamics,relative coordinates and graph theory are combined to analyze the structure of a vehicle suspension.The dynamic equations of the left front suspension system are derived for modeling.First,The pure tire theory model is used as the input criteria of the suspension multibody system dynamic model in order to simulate the suspension K&C characteristics test.Then,it is important to verify the accuracy of this model by comparing and analyzing the experimental data and simulation results.The results show that the model has high precision and can predict the performance of the vehicle.It also provides a new solution for the vehicle dynamic modeling.

Effect of graph generation on slope stability analysis based on graph theory

Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.

A graph theory model using human nature structure

A graph theory model of the human nature structure( GMH) for machine vision and image/graphics processing is described in this paper. Independent from the motion and deformation of contours,the human nature structure( HNS) embodies the most basic movement characteristics of the body. The human body can be divided into basic units like head,torso,and limbs. Using these basic units,a graph theory model for the HNS can be constructed. GMH provides a basic model for human posture processing,and the outline in the perspective projection plane is the body contour of an image. In addition,the GMH can be applied to articulated motion and deformable objects,e. g.,in the design and analysis of body posture,by modifying mapping parameters of the GMH.

Graph Theory and Matrix Approach(GTMA)Model for the Selec­tion of the Femoral-Component of Total Knee Joint Replacement

Total Knee Replacement(TKR)is the increasing trend now a day,in revision surgery which is associated with aseptic loosening,which is a challenging research for the TKR component.The selection of optimal material loosening can be controlled at some limits.This paper is going to consider the best material selected among a number of alternative materials for the femoral component(FC)by using Graph Theory.Here GTMA process used for optimization of material and a systematic technique introduced through sensitivity analysis to find out the more reliable result.Obtained ranking suggests the use of optimized material over the other existing material.By following GTMA Co_Cr-alloys(wrought-Co-Ni-Cr-Mo)and Co_Cr-alloys(cast-able-Co-Cr-Mo)are on the 1st and 2nd position respectively.

Optimization of Grouping Evacuation Strategy in High-rise Building Fires Based on Graph Theory and Computational Experiments

It is difficult to rescue people from outside, and emergency evacuation is still a main measure to decrease casualties in high-rise building fires. To improve evacuation efficiency, a valid and easily manipulated grouping evacuation strategy is proposed. Occupants escape in groups according to the shortest evacuation route is determined by graph theory. In order to evaluate and find the optimal grouping, computational experiments are performed to design and simulate the evacuation processes. A case study shown the application in detail and quantitative research conclusions is obtained. The thoughts and approaches of this study can be used to guide actual high-rise building evacuation processes in future.

A Computational Synthesis Approach of Mechanical Conceptual Design Based on Graph Theory and Polynomial Operation

The design synthesis is the key issue in the mechanical conceptual design to generate the design candidates that meet the design requirements.This paper devotes to propose a novel and computable synthesis approach of mechanisms based on graph theory and polynomial operation.The graph framework of the synthesis approach is built firstly,and it involves:(1)the kinematic function units extracted from mechanisms;(2)the kinematic link graph that transforms the synthesis problem from mechanical domain into graph domain;(3)two graph representations,i.e.,walk representation and path representation,of design candidates;(4)a weighted matrix theorem that transforms the synthesis process into polynomial operation.Then,the formulas and algorithm to the polynomial operation are presented.Based on them,the computational flowchart to the synthesis approach is summarized.A design example is used to validate and illustrate the synthesis approach in detail.The proposed synthesis approach is not only supportive to enumerate the design candidates to the conceptual design of a mechanical system exhaustively and automatically,but also helpful to make that enumeration process computable.

Alterations of Cerebral Functional Connectivity in Patients with Frontal Lobe Epilepsy:A Graph Theory Study

The aim of the present study is to investigate the brain functional network changes of patients with frontal lobe epilepsy(FLE)by resting-state functional magnetic resonance imaging(rsfMRI)and graph theoretical analysis.rsfMRI is performed in 46 adult patients with FLE and 46 age matched healthy controls(HCs).A functional network is built from these subjects,and the topological properties of such network are analyzed quantitatively using graph theoretical methods.According to the results,both FLE patients and HCs exhibit prominent small world features.Compared with HCs,FLE shows a decrease in local efficiency(Eloc),clustering coefficient,nodal efficiency as well as nodal degree.Furthermore,FLE(seven)has fewer hubs than HCs(ten).The functional abnormalities in the network organization suggest functional disturbances in patients with FLE.This study helps to gain new insights into the functional disorder in patients with FLE.The networks built here can also be a set of potential biomarkers for the diagnosis,monitoring and the treatment of FLE.

Applications of Graph Theory to Gross Error Detection for GPS Geodetic Control Networks

This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components.In this algorithm the gross error detection is undertaken through loops of different spanning trees using the "Loop Law" in which the individual components Δ X, Δ Y and Δ Z sum up to zero.If the sum of the respective vector components ∑X,∑Y and ∑Z in a loop is not zero and if the error is beyond the tolerable limit (ε>w),it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re_observed.After successful screening of errors by graph theory,network adjustment can be carried out.In this paper,the GPS data from the control network established as reference system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm.

INTERFERENCE COORDINATION METHOD BASED ON GRAPH THEORY IN TWO-TIER CELLULAR NETWORKS

This paper studies an interference coordination method by means of spectrum allocation in Long-Term Evolution (LTE) multi-cell scenario that comprises of macrocells and femtocells. The purpose is to maximize the total throughput of femtocells while ensuring the Signal-to-Interference plus Noise Ratio (SINR) of the edge macro mobile stations (mMSs) and the edge femtocell Mobile Stations (fMSs). A new spectrum allocation algorithm based on graph theory is proposed to reduce the interference. Firstly, the ratio of Resource Blocks (RBs) that mMSs occupy is obtained by genetic algorithm. Then, after considering the impact of the macro Base Stations (mBSs) and small scale fading to the fMS on different RBs, multi-interference graphs are established and the spectrum is allocated dynamically. The simulation results show that the proposed algorithm can meet the Quality of Service (QoS) requirements of the mMSs. It can strike a balance between the edge fMSs' throughput and the whole fMSs' throughput.

FastCluster: a graph theory based algorithm for removing redundant sequences

In many cases, biological sequence databases contain redundant sequences that make it difficult to achieve reliable statistical analysis. Removing the redundant sequences to find all the real protein families and their representatives from a large sequences dataset is quite important in bioinformatics. The problem of removing redundant protein sequences can be modeled as finding the maximum independent set from a graph, which is a NP problem in Mathematics. This paper presents a novel program named FastCluster on the basis of mathematical graph theory. The algorithm makes an improvement to Hobohm and Sander’s algorithm to generate non-redundant protein sequence sets. FastCluster uses BLAST to determine the similarity between two sequences in order to get better sequence similarity. The algorithm’s performance is compared with Hobohm and Sander’s algorithm and it shows that Fast- Cluster can produce a reasonable non-redundant pro- tein set and have a similarity cut-off from 0.0 to 1.0. The proposed algorithm shows its superiority in generating a larger maximal non-redundant (independent) protein set which is closer to the real result (the maximum independent set of a graph) that means all the protein families are clustered. This makes Fast- Cluster a valuable tool for removing redundant protein sequences.

Basic Concepts of Graph Theory as the Instruments of Mathematical Formalization of Woven Structures

The paper presents the prerequisites of involving of topological elements and graph theory as an instrument of mathematical formalization of woven structures and technology of textile fabrics. Present research is based on analysis and comparison of the main concepts and conditions of textile technology and graph theory.

Fault Diagnosis Based on Graph Theory and Linear Discriminant Principle in Electric Power Network

In this paper, we adopt a novel topological approach to fault diagnosis. In our researches, global information will be introduced into electric power network, we are using mainly BFS of graph theory algorithms and linear discriminant principle to resolve fast and exact analysis of faulty components and faulty sections, and finally accomplish fault diagnosis. The results of BFS and linear discriminant are identical. The main technical contributions and innovations in this paper include, introducing global information into electric power network, developing a novel topological analysis to fault diagnosis. Graph theory algorithms can be used to model many different physical and abstract systems such as transportation and communication networks, models for business administration, political science, and psychology and so on. And the linear discriminant is a procedure used to classify an object into one of several a priori groupings dependent on the individual characteristics of the object. In the study of fault diagnosis in electric power network, graph theory algorithms and linear discriminant technology must also have a good prospect of application.

An interactive approach for generating spatial architecture layout based on graph theory

This study proposes a graph theory based method for generating three-dimensional architectural layouts on the target of creating space that provides rich perceptual experience.The proposed approach incorporates the decisions of architects in the generation process to improve efficiency and avoid invalid results.Space is interpreted as a combination of volumes adjacent to,intersecting with or containing each other and is represented by a graph with nodes and edges.The study first generates an orthogonal orientation digraph(OODG),which denotes the relative positions of spaces and provides options for users to decide whether to continue generating the layout.Based on a given OODG,a combination of connected volumes is generated.The generation results show that the proposed method can generate space providing a rich experience when relations between volumes are properly set.

A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

Algorithm for Visualization of Zero Divisor Graphs of the Ring ℤn Using MAPLE Coding

This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.

Fault-line selection and fault-type recognition in DC systems based on graph theory

When a fault occurs in a DC system,the fault current rises rapidly with no zero-crossing point which makes fault-line selection and fault-type identification difficult.In this paper,an online detection and protection method based on graph theory,namely the“double D method”,is proposed for fault-line selection and fault-type identification in DC systems.In the proposed method,the entire distribution network is visualized as a“map”with vertices representing the line convergence points and edges representing the connection lines.A network topology matrix“D”is formed by detecting the current directions as the current directions are altered following a fault,whereas the current directions at the ends of non-fault lines remain the same.In order to prevent misjudgment problems arising from power flow reversal,the rates of change of the fault currents are used to further determine whether a fault has occurred and the“double D method”is introduced to identify the fault type.Simulations results with different fault types verify the effectiveness and reliability of the proposed method.