scholarly journals A graph theory approach of the study of macroeconomics networks

2017 ◽  
Author(s):  
Γεώργιος-Αντώνιος Σαραντίτης
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Dominating Set ◽  
Theory Approach ◽  
Minimum Dominating Set

Πολλά σύγχρονα οικονομικά συστήματα χαρακτηρίζονται από αυξημένο βαθμό πολυπλοκότητας. Οι οντότητες αυτών των συστημάτων αναπτύσσουν διακριτές, αναδυόμενες και μη γραμμικές συμπεριφορές που δεν μπορούν να περιγραφούν πλήρως με οικονομετρικές τεχνικές. Τα τελευταία χρόνια, λόγω της γρήγορης αύξησης της υπολογιστικής ισχύος και της εξέλιξης των αλγορίθμων, η επιστήμη της Ανάλυσης Δικτύων ενσωματώθηκε στην ανάλυση τέτοιων πολύπλοκων οικονομικών συστημάτων, συμπληρώνοντας τη χρήση της οικονομετρίας.Μια κοινώς χρησιμοποιούμενη τεχνική στο πλαίσιο της Ανάλυσης Δικτύων είναι το Minimum Spanning Tree (MST). Το MST παράγει ένα υπο-δίκτυο του αρχικού δικτύου στο οποίο είναι συνδεδεμένοι όλοι οι κόμβοι έτσι ώστε να μην υπάρχουν βρόχοι. Ωστόσο, το MST φέρει κάποια εγγενή μειονεκτήματα που προέρχονται άμεσα από τη διαδικασία αλγοριθμικού προσδιορισμού του και μπορεί να το καταστήσουν ακατάλληλο για τη μελέτη οικονομικών δικτύων. Αυτή η διατριβή αποσκοπεί στο να αναδείξει τα μειονεκτήματα του MST όταν χρησιμοποιείται στα οικονομικά δίκτυα και να επισημάνει τα πλεονεκτήματα μιας νέας τεχνικής βελτιστοποίησης, που ονομάζεται Threshold-Minimum Dominating Set (T-MDS) ως μια καταλληλότερη λύση. Επιπλέον, εισάγεται το Threshold Weighted - Minimum Dominating Set (TW-MDS), το οποίο διατηρεί όλα τα πλεονεκτήματα του T-MDS και, ανάλογα με το δεδομένο σύνολο, μπορεί να είναι πιο κατάλληλο για διαχρονικές αναλύσεις που εκτελούνται στην πάροδο του χρόνου.Η ανωτερότητα των T-MDS και TW-MDS σε σχέση με το κλασικό MST αρχικά επισημαίνεται σε αυτή τη διατριβή με κατάλληλα θεωρητικά παραδείγματα. Στη συνέχεια συνεχίζουμε παρέχοντας ένα ευρύ φάσμα μακροοικονομικών εφαρμογών: τον συγχρονισμό των οικονομικών κύκλων, την εξέλιξη της ανισότητας εισοδήματος και τη μέτρηση του πληθωρισμού πυρήνα. Με αυτόν τον τρόπο τονίζουμε την καταλληλότητα των προτεινόμενων μεθοδολογιών στη μακροοικονομική ανάλυση. Έτσι, αυτή η διατριβή έχει διπλή συμβολή στην ανάλυση των σύνθετων οικονομικών δικτύων: από τη θεωρητική πλευρά επεκτείνει τη σχετική βιβλιογραφία παρέχοντας ένα πιο κατάλληλο εργαλείο από αυτό που χρησιμοποιείται προς το παρόν, ενώ από την εμπειρική πλευρά παρέχει νέα αποτελέσματα από τις διαφορετικές οικονομικές Εφαρμογές του T-MDS.

Interrelationships Among the Liliatae: a Graph Theory Approach

1980 ◽  
Vol 28 (2) ◽  
pp. 261 ◽  
Author(s):  
HT Clifford ◽  
WT Williams
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Theory Approach ◽  
Nearest Neighbours ◽  
Shared Ancestry ◽  
Evolutionary Convergence

The interrelationships of the families of Liliatae were investigated by using a network generating program (NETS) which, unlike minimum spanning tree programs, considers both first and second nearest neighbours. Within the resultant network the distribution of families reflects many traditionally accepted assemblages, including the Zingiberales and Alismatales. The affinities of the Arecaceae in particular suggests that the observed similarities between some families may be due to evolutionary convergence rather than to a shared ancestry. This fact, plus the tendency of the network to branch rather than to form loops, helps to account for the difficulty in classifying the class.

Mathematical Modelling for Transportation With Application to Airline Transportation Network

2021 ◽  
pp. 28-51
Author(s):  
Sadiqah Almarzooq ◽  
Njwd Albishi
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Transportation Networks ◽  
Transportation Network ◽  
Weighted Graph ◽  
Search Method ◽  
Nearest Neighbour ◽  
Water Pipelines ◽  
Regional Airports

Graph theory is a basic tool to solve real-world problems such as communication between people, water pipelines, and transportation networks. A transportation network can be modeled as connected weighted graph. This chapter starts by introducing some fundamental concepts of graph theory to be applied to three main problems: the minimum spanning tree, the shortest path, and the travel salesperson. The authors discuss some appropriated algorithms such as depth first algorithm, Prim's algorithm, Kruskal's algorithm, Dijkstra's algorithm, the nearest neighbour algorithm, the minimum spanning tree depth first search method (MST-DFS) algorithm, and the Christofides' algorithm to solve these problems and apply them the airlines network between international and regional airports in Saudi Arabia.

scholarly journals The Use of Weighted Adjacency Matrix for Searching Optimal Transportation Routes

2018 ◽  
Author(s):  
Karel Antoš
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Optimal Transportation ◽  
New Approach ◽  
New Variant ◽  
Transportation Routes ◽  
Weighted Adjacency Matrix

This article provides a new approach to searching solutions of the ship transport optimalization problems. It brings a new variant of one algorithm of searching for the Minimum Spanning Tree. The new element in the algorithm is that it uses the Weighted Adjacency Matrix. This Weighted Adjacency Matrix is suitable for searching for the Minimum Spanning Tree (MST) of the graph. It shows how it could be used in cases where weighted edges of the graph are given. This creates a new procedure of searching for the MST of the graph and completes previously known algorithms of searching for the MST. In the field of transportation it could be succesfully used for solutions of optimizing transportation routes where smallest costs are wanted. Proposed Weighted Adjacency Matrix could be used in similar issues in the field of the graph theory, where graphs with weighted edges are given. The procedure is shown on the attached example.

scholarly journals ALGORITMA “HANCURKAN SEMUA SIKEL” UNTUK MENENTUKAN POHON PERENTANG MINIMUM DARI SUATU GRAF BERBOBOT

2019 ◽  
Vol 21 (2) ◽  
pp. 91-98
Author(s):  
Ricky Aditya
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Weighted Graph ◽  
Alternative Algorithm

The minimum spanning tree is one of the applications of graph theory in various fields. There are several algorithms for determining the minimum spanning tree of a weighted graph, such as Kruskal's algorithm and Prim's algorithm. These two algorithms are not really easy to teach to students in general. Therefore in this paper presented an alternative algorithm called the algorithm "Destroy All Sikel", which is more intuitive and easier to understand. Furthermore, there are also examples of implementation and comparison with two other algorithms.

scholarly journals Graph Theory Approach to the Vulnerability of Transportation Networks

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 270
Author(s):  
Sambor Guze
Keyword(s):  
Graph Theory ◽  
Large Scale ◽  
Transportation Networks ◽  
Transportation Network ◽  
Dominating Set ◽  
Transport Sector ◽  
Critical Element ◽  
Theory Approach ◽  
Dominating Sets ◽  
Transport Networks

Nowadays, transport is the basis for the functioning of national, continental, and global economies. Thus, many governments recognize it as a critical element in ensuring the daily existence of societies in their countries. Those responsible for the proper operation of the transport sector must have the right tools to model, analyze, and optimize its elements. One of the most critical problems is the need to prevent bottlenecks in transport networks. Thus, the main aim of the article was to define the parameters characterizing the transportation network vulnerability and select algorithms to support their search. The parameters proposed are based on characteristics related to domination in graph theory. The domination, edge-domination concepts, and related topics, such as bondage-connected and weighted bondage-connected numbers, were applied as the tools for searching and identifying the bottlenecks in transportation networks. Furthermore, the algorithms for finding the minimal dominating set and minimal (maximal) weighted dominating sets are proposed. This way, the exemplary academic transportation network was analyzed in two cases: stationary and dynamic. Some conclusions are presented. The main one is the fact that the methods given in this article are universal and applicable to both small and large-scale networks. Moreover, the approach can support the dynamic analysis of bottlenecks in transport networks.

scholarly journals Penentuan Rute Terpendek Jalur Distribusi Air Artesis Menggunakan Kruskal

2018 ◽  
Vol 2 (2) ◽  
pp. 121
Author(s):  
Diah Ayu Retnani Wulandari ◽  
Fajrin Nurman Arifin
Keyword(s):  
Graph Theory ◽  
Water Supply ◽  
Water Flow ◽  
Shortest Path ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Flow Distribution ◽  
Path Optimization ◽  
Network Method ◽  
Artesian Water

Water flow distribution to home residents from the artesian well is affected by infrastructure. The more houses that distributed makes decreased amount supply of artesian water in every house. the longer of pipe leight and many branches traversed makes decrease of water supply because there will be many possible pipeline leaks. The more pipes used make the more expensive infrastructure cost. This problem occurs in Jubung area. These problems is one variation of the minimum Spanning Tree problems. This problem can be solved by the shortest path optimization route. It uses network method by implementing graph theory through kruskal algorithm. The first step is determined the nodes and sides. Nodes represent house and the sides represents the connecting pipes between houses. Kruskal is chosen because the kruskal focuses on the side and the graph is incomplete. focus of this study is the length optimation of the connecting pipe that is represented by side. In the pipe infrastructure figure map is representing of an incomplete graph because there are several nodes that are not connected to all nodes because it is adapted to the contour of the land that is not possible traversed the pipe. The results is there are several paths that are changed, especially the side to connect between node 1-4, 4-12, 19-20, 21-6 dispensed because forming cycles. The result of this research is kruskal can make decreasing infrastrukture cost Rp.7.535.500 with length of 201,5 meter so can save Rp.4.401.000 from Rp Rp.11.936.500.

scholarly journals A Graph Theory Approach on Cryptography

2018 ◽  
Vol 2 (1) ◽  
pp. 97-104
Author(s):  
Nandhini R ◽  
Maheswari V ◽  
Balaji V
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Theory Approach

In this paper, we discuss about the connection between graph theory and cryptography. We use the spanning tree concept of graph theory to encryption the message.

scholarly journals Proposal of creation of a portfolio with minimal risk

2017 ◽  
Vol 14 (2) ◽  
pp. 107-115 ◽  
Author(s):  
Vincent Šoltés ◽  
Jakub Danko
Keyword(s):  
Graph Theory ◽  
Standard Deviation ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Stock Index ◽  
Discrete Mathematics ◽  
Second Step ◽  
Minimal Risk ◽  
Investment Strategies ◽  
Individual Investor

The aim of this work is to propose a method for creating portfolios with a minimal expected risk. The proposed method consists of two steps. In the first step, the authors use a method for finding a minimum spanning tree. It is a graph theory tool, which is the field of discrete mathematics. Graph is defined as a set of vertices and edges. By this method the authors distribute assets, for example a stock index, into several subgroups. From each group it is then chosen an asset, from which most of the edges come out. These selected assets will be used to create a portfolio. In the second step, the authors will use a method of minimizing the standard deviation of the portfolio to calculate the weight of its assets. By this method, first it is found the weight of each asset so that the resulting portfolio would have the lowest possible expected risk. Then the authors find the portfolio with the lowest possible expected risk at required yield and create investment strategies. These strategies are compared during the time and between each other based on the variation coefficient. The article can be a practical guide for an individual investor during the minimal risk portfolio creation and shows him, which assets (and which asset weights) of the selected index to purchase.

scholarly journals PENERAPAN TEORI GRAF UNTUK MENYELESAIKAN MASALAH MINIMUM SPANNING TREE (MST) MENGGUNAKAN ALGORITMA KRUSKAL

2012 ◽  
Vol 1 (2) ◽  
Author(s):  
Swaditya Rizki
Keyword(s):  
Communication Network ◽  
Graph Theory ◽  
Complete Graph ◽  
Network Optimization ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Optimization Problems ◽  
Source Code ◽  
Basic Algorithm ◽  
Communication Network Design

One of useful graph theory to solve the real problems is Minimum Spanning Tree (MST). MST is network optimization problems that can be applied in many fields such as transportations problems and communication network design (Gruber and Raidl, 2005). MST begins from tree namely a connected graph has no circuits. From the graph, there is a sub-graph that has all the vertex or spanning tree. If that graph has the weight/cost, then the spanning tree that has the smallest weight/cost is called Minimum Spanning Tree. Basic algorithm used to determine the MST is Kruskal’s algorithm. This algorithm is known as one of the best algorithms for the optimization problems, especially for MST. In this paper is developed a source code program to determine MST using Kruskal’s algorithm and then implemented on several data representing a complete graph.

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