scholarly journals Graphs in Network Flows

2012 ◽  
Vol 11 (4) ◽  
pp. 99-108
Author(s):  
V Manjula
Keyword(s):  
Network Flow ◽  
Network Flows ◽  
Real Life ◽  
Maximum Flow ◽  
Modern World ◽  
Circuit Boards ◽  
Graph Theoretic ◽  
Life Problems ◽  
Theoretic Problem ◽  
Flow Of Information

This paper presents a collection of basics and application of Network flows in Graph theory which is an out- growth of set of lecture notes on Graph applications. It is not only a record of material from text books but also a reflection of precise graphical concept which will be useful for students where such facts are needed. There are many real life problems dealing with discrete objects and binary relations and graph is very convenient form of its representation. A network flow graph G=(V,E) is a directed graph with two special vertices: the source vertex s, and the sink vertex t. Many problems in the real world are to be solved using maximum flow. "Real" networks, like the Internet or electronic circuit boards, are good examples of flow networks. Generally graphs can be used in two situations. Firstly since graph is a very simple, convenient and natural way of representing the relationship between objects. Secondly we have graph as model solve the appropriate graph theoretic problem then interpret the solution in terms of original problem In the modern world, planning efficient routes is essential for business and industry, The flow of information or water or gas etc in a network are useful to find the max rate of flow that is possible from one station to another A Transport network represents a general model for transportation of material from origin of supply to destination through shipping routes. The objective of this paper is to discuss the concepts and terminology of Network flows with Graphical representations.

Introduction

2021 ◽  
pp. 1-36
Author(s):  
Vadim Zverovich
Keyword(s):  
Graph Theory ◽  
Biological Networks ◽  
Real Life ◽  
Scale Free ◽  
Graph Theoretic ◽  
Life Problems ◽  
Scale Free Networks ◽  
Web Graph ◽  
The Web

This chapter gives a brief overview of selected applications of graph theory, many of which gave rise to the development of graph theory itself. A range of such applications extends from puzzles and games to serious scientific and real-life problems, thus illustrating the diversity of applications. The first section is devoted to the six earliest applications of graph theory. The next section introduces so-called scale-free networks, which include the web graph, social and biological networks. The last section describes a number of graph-theoretic algorithms, which can be used to tackle a number of interesting applications and problems of graph theory.

scholarly journals Connectivity Indices of Intuitionistic Fuzzy Graphs and Their Applications in Internet Routing and Transport Network Flow

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Tulat Naeem ◽  
Abdu Gumaei ◽  
Muhammad Kamran Jamil ◽  
Ahmed Alsanad ◽  
Kifayat Ullah
Keyword(s):  
Network Flow ◽  
Real Life ◽  
Vital Role ◽  
Transport Network ◽  
Internet Routing ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Connectivity Indices ◽  
Intuitionistic Fuzzy Graphs

Connectivity index CI has a vital role in real-world problems especially in Internet routing and transport network flow. Intuitionistic fuzzy graphs IFGs allow to describe two aspects of information using membership and nonmembership degrees under uncertainties. Keeping in view the importance of CI s in real life problems and comprehension of IFGs , we aim to develop some CI s in the environment of IFGs . We introduce two types of CI s , namely, CI and average CI , in the frame of IFGs . In spite of that, certain kinds of nodes called IF connectivity enhancing node IFCEN , IF connectivity reducing node IFCRN , and IF neutral node are introduced for IFGs . We have introduced strongest strong cycles, θ -evaluation of vertices, cycle connectivity, and CI of strong cycle. Applications of the CI s in two different types of networks are done, Internet routing and transport network flow, followed by examples to show the applicability of the proposed work.

scholarly journals Analysis of the Shortest Path in Spherical Fuzzy Networks Using the Novel Dijkstra Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Zafar Ullah ◽  
Huma Bashir ◽  
Rukhshanda Anjum ◽  
Salman A. AlQahtani ◽  
Suheer Al-Hadhrami ◽  
...  
Keyword(s):  
Shortest Path ◽  
Real Life ◽  
Graphical Analysis ◽  
The Novel ◽  
Fuzzy Graph ◽  
Dijkstra Algorithm ◽  
Shortest Path Problems ◽  
Graph Theoretic ◽  
Life Problems ◽  
Novel Concept

The concept of fuzzy graph (FG) and its generalized forms has been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems, and so on. This paper is based on some developments in generalization of FG theory to deal with situation where imprecision is characterized by four types of membership grades. A novel concept of T-spherical fuzzy graph (TSFG) is proposed as a common generalization of FG, intuitionistic fuzzy graph (IFG), and picture fuzzy graph (PFG) based on the recently introduced concept of T-spherical fuzzy set (TSFS). The significance and novelty of proposed concept is elaborated with the help of some examples, graphical analysis, and results. Some graph theoretic terms are defined and their properties are studied. Specially, the famous Dijkstra algorithm is proposed in the environment of TSFGs and is applied to solve a shortest path problem. The comparative analysis of the proposed concept and existing theory is made. In addition, the advantages of the proposed work are discussed over the existing tools.

scholarly journals A Review of Flow-Capacitated Networks: Algorithms, Techniques and Applications

2021 ◽  
pp. 1-33
Author(s):  
Omar Mutab Alsalami ◽  
Ali Muhammad Ali Rushdi
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Maximum Flow ◽  
Flow Properties ◽  
Transformation Techniques ◽  
Graph Theoretic ◽  
Network Problems ◽  
Definition Of ◽  
Capacitated Network ◽  
Alternative Solutions

This paper presents a review of flow network concepts, including definition of some graph-theoretic basics and a discussion of network flow properties. It also provides an overview of some crucial algorithms used to solve the maximum-flow problem such as the Ford and Fulkerson algorithm (FFA), supplemented with alternative solutions, together with the essential terminology for this algorithm. Moreover, this paper explains the max-flow min-cut theorem in detail, analyzes the concepts behind it, and provides some examples and their solutions to demonstrate this theorem. As a bonus, it expounds the reduction and transformation techniques used in a capacitated network. In addition, this paper reviews one of the popular techniques for analyzing capacitated networks, which is the “decomposition technique”. This technique is centered on conditioning a complicated network on the possible states of a keystone element  or on the possible combinations of states of many keystone elements. Some applications of capacitated network problems are addressed based on each type of problem being discussed.

The Psychologist in the Medical School: An Example of Solving Real-Life Problems

1970 ◽  
Author(s):  
Matisyohu Weisenberg ◽  
Carl Eisdorfer ◽  
C. Richard Fletcher ◽  
Murray Wexler
Keyword(s):  
Medical School ◽  
Real Life ◽  
Life Problems

scholarly journals Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1716
Author(s):  
Adrian Marius Deaconu ◽  
Delia Spridon
Keyword(s):  
Network Flow ◽  
Large Scale ◽  
Random Network ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Network Flow Problems ◽  
Commodity Flow ◽  
Vast Number ◽  
Flow Problems ◽  
Execution Speed

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

scholarly journals AnANN Model Trained on Regional Data in the Prediction of Particular Weather Conditions

2021 ◽  
Vol 11 (11) ◽  
pp. 4757
Author(s):  
Aleksandra Bączkiewicz ◽  
Jarosław Wątróbski ◽  
Wojciech Sałabun ◽  
Joanna Kołodziejczyk
Keyword(s):  
Atmospheric Pressure ◽  
Real Life ◽  
Real Data ◽  
Weather Conditions ◽  
Maximum Temperature ◽  
Air Masses ◽  
Weather Forecasts ◽  
Life Problems ◽  
The World ◽  
The City

Artificial Neural Networks (ANNs) have proven to be a powerful tool for solving a wide variety of real-life problems. The possibility of using them for forecasting phenomena occurring in nature, especially weather indicators, has been widely discussed. However, the various areas of the world differ in terms of their difficulty and ability in preparing accurate weather forecasts. Poland lies in a zone with a moderate transition climate, which is characterized by seasonality and the inflow of many types of air masses from different directions, which, combined with the compound terrain, causes climate variability and makes it difficult to accurately predict the weather. For this reason, it is necessary to adapt the model to the prediction of weather conditions and verify its effectiveness on real data. The principal aim of this study is to present the use of a regressive model based on a unidirectional multilayer neural network, also called a Multilayer Perceptron (MLP), to predict selected weather indicators for the city of Szczecin in Poland. The forecast of the model we implemented was effective in determining the daily parameters at 96% compliance with the actual measurements for the prediction of the minimum and maximum temperature for the next day and 83.27% for the prediction of atmospheric pressure.

scholarly journals Formulating Modes of Cooperative Leaning for Education for Sustainable Development

2021 ◽  
Vol 13 (6) ◽  
pp. 3465
Author(s):  
Jordi Colomer ◽  
Dolors Cañabate ◽  
Brigita Stanikūnienė ◽  
Remigijus Bubnys
Keyword(s):  
Sustainable Development ◽  
Real Life ◽  
Education For Sustainable Development ◽  
Professional Life ◽  
Global Challenges ◽  
Life Problems ◽  
The Face ◽  
Contemporary Education ◽  
The Impact

In the face of today’s global challenges, the practice and theory of contemporary education inevitably focuses on developing the competences that help individuals to find meaningfulness in their societal and professional life, to understand the impact of local actions on global processes and to enable them to solve real-life problems [...]

Review of Network Flow Algorithms David P. Williamson

2021 ◽  
Vol 52 (1) ◽  
pp. 12-15
Author(s):  
S.V. Nagaraj
Keyword(s):  
Graduate Students ◽  
Real World ◽  
Network Flow ◽  
Network Flows ◽  
Optimization Problems ◽  
Capacity Constraints ◽  
Incoming Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Real World Problems

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

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