scholarly journals Network Theory and Switching Behaviors: A User Guide for Analyzing Electronic Records Databases

2021 ◽  
Vol 13 (9) ◽  
pp. 228
Author(s):  
Giorgio Gronchi ◽  
Marco Raglianti ◽  
Fabio Giovannelli
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Network Theory ◽  
Clustering Algorithms ◽  
Switching Behavior ◽  
Electronic Records ◽  
Behavior Patterns ◽  
Control Groups ◽  
Drug Switching ◽  
Basic Concepts

As part of studies that employ health electronic records databases, this paper advocates the employment of graph theory for investigating drug-switching behaviors. Unlike the shared approach in this field (comparing groups that have switched with control groups), network theory can provide information about actual switching behavior patterns. After a brief and simple introduction to fundamental concepts of network theory, here we present (i) a Python script to obtain an adjacency matrix from a records database and (ii) an illustrative example of the application of network theory basic concepts to investigate drug-switching behaviors. Further potentialities of network theory (weighted matrices and the use of clustering algorithms), along with the generalization of these methods to other kinds of switching behaviors beyond drug switching, are discussed.

scholarly journals Structural Analysis of Bus Networks Using Indicators of Graph Theory and Complex Network Theory

2017 ◽  
Vol 11 (1) ◽  
pp. 92-100 ◽  
Author(s):  
Hui Zhang
Keyword(s):  
Graph Theory ◽  
Complex Network ◽  
Adjacency Matrix ◽  
Network Theory ◽  
Weighted Average ◽  
Power Law Distribution ◽  
Complex Network Theory ◽  
Path Distance ◽  
Bus Network ◽  
Bus Networks

The structure of bus network is very significant for bus system. To evaluate the performance of the structure of bus network, indicators basing on graph theory and complex network theory are proposed. Three forms of matrices comprising line-station matrix, weighted adjacency matrix and adjacency matrix under space P are used to represent the bus network. The paper proposes a shift power law distribution which is related average degree of network to fit the degree distribution and a method to calculate the average transfer time between any two stations using adjacency matrix under P space. Moreover, this paper proposes weighted average shortest path distance and transfer efficiency to evaluate the bus network. The results show that the indicators that we introduce, effectively reflect properties of bus network.

scholarly journals Probability of an Intermediate (Reduced Operational) State

2021 ◽  
Vol 12 (3) ◽  
pp. 71-96
Author(s):  
Paweł SZCZEPAŃSKI
Keyword(s):  
Graph Theory ◽  
Intermediate State ◽  
Single Element ◽  
Additional Component ◽  
Kolmogorov Equations ◽  
The Subject ◽  
Basic Concepts ◽  
Operational Failure

This work examines with the form of the well-known sum: p + q = 1 – which is the sum of the probabilities of opposite events, in particular: the sum of the probabilities of the operational and non-operational (failure) states of a single element (a creation characterised by one output and any number of inputs). It was found that without significantly compromising the accuracy of the previous analyses, it was possible to introduce an additional component to the sum: iiipq3, a component that embodies the probability of an intermediate state, or a reduced operational state. With a constant value of the sum of the components in question, their variation as a function of probability q was determined, following which in the function of the same variable the variation of the entropy of an element's i state was examined using Chapman-Kolmogorov equations; here the focus was on investigating the intensity of the transition from the operational state to the non-operational state or an intermediate state, and from an intermediate state to the non-operational state. The meaning of intermediate probability was also referenced to the object: its diagnostic program, the entropy of structure, the full set of discriminable states, and the relevant transition intensities. It became indispensable in this respect to describe the object using the language of graph theory, in which the basic concepts are layers and an availability matrix. It should be noted that the subject object is an entity that comprises a set of individual elements, with a number and structure of connections that are consistent with the purpose of this entity.

scholarly journals COLLEGE STUDENT’S ERROR ANALYSIS BASED ON THEIR MATHEMATICAL CONNECTIONS ON GRAPH REPRESENTATION

2019 ◽  
Vol 4 (1) ◽  
pp. 18
Author(s):  
I ketut Suastika ◽  
Vivi Suwanti
Keyword(s):  
Graph Theory ◽  
College Student ◽  
Real Life ◽  
Graph Representation ◽  
High Ability ◽  
Pilot Studies ◽  
Graph Representations ◽  
Mathematical Connections ◽  
Life Problems ◽  
Basic Concepts

This study is investigates the college student’s errors on their graph representations making based on the mathematical connections indicators. Pilot studies were conducted with 4 college students of middle to high ability in Graph Theory class. Data analyze revealed that top 3 subject’s errors are 1) Finding the relations of a representations to it’s concepts and procedures, 2) Applying mathematics in other sciences or real life problems, and 3) Finding relations among procedures of the equivalent representations. Their lack of graph concepts understanding and it’s connections plays the major role in their errors. They failed at recognizing and choosing the suitable properties of graph which able to detect the error of their graph representation. So, in order to decrease college student errors in graph representations, we need to strengthen their basic concepts and its connections.

Graph Theory

2020 ◽  
pp. 354-370
Author(s):  
Seethalakshmi R.
Keyword(s):  
Graph Theory ◽  
Market Structure ◽  
Financial Market ◽  
Network Theory ◽  
Financial Analysts ◽  
Structural Models ◽  
Topological Properties ◽  
Strategic Decisions ◽  
Analytical Geometry ◽  
Innovative Methods

Mathematics acts an important and essential need in different fields. One of the significant roles in mathematics is played by graph theory that is used in structural models and innovative methods, models in various disciplines for better strategic decisions. In mathematics, graph theory is the study through graphs by which the structural relationship studied with a pair wise relationship between different objects. The different types of network theory or models or model of the network are called graphs. These graphs do not form a part of analytical geometry, but they are called graph theory, which is points connected by lines. The various concepts of graph theory have varied applications in diverse fields. The chapter will deal with graph theory and its application in various financial market decisions. The topological properties of the network of stocks will provide a deeper understanding and a good conclusion to the market structure and connectivity. The chapter is very useful for academicians, market researchers, financial analysts, and economists.

Finite Characterization of the Coarsest Balanced Coloring of a Network

2020 ◽  
Vol 30 (14) ◽  
pp. 2050212
Author(s):  
Ian Stewart
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Universal Cover ◽  
Running Time ◽  
Set Up ◽  
Balanced Coloring ◽  
Refinement Algorithm ◽  
Partition Refinement

Balanced colorings of networks correspond to flow-invariant synchrony spaces. It is known that the coarsest balanced coloring is equivalent to nodes having isomorphic infinite input trees, but this condition is not algorithmic. We provide an algorithmic characterization: two nodes have the same color for the coarsest balanced coloring if and only if their [Formula: see text]th input trees are isomorphic, where [Formula: see text] is the number of nodes. Here [Formula: see text] is the best possible. The proof is analogous to that of Leighton’s theorem in graph theory, using the universal cover of the network and the notion of a symbolic adjacency matrix to set up a partition refinement algorithm whose output is the coarsest balanced coloring. The running time of the algorithm is cubic in [Formula: see text].

Binomial incidence matrix of a semigraph

2020 ◽  
pp. 2150017
Author(s):  
Jyoti Shetty ◽  
G. Sudhakara
Keyword(s):  
Graph Theory ◽  
Complete Graph ◽  
Adjacency Matrix ◽  
Incidence Matrix ◽  
Systematic Approach ◽  
Line Graph ◽  
The Matrix ◽  
Theory Of Graphs

A semigraph, defined as a generalization of graph by  Sampathkumar, allows an edge to have more than two vertices. The idea of multiple vertices on edges gives rise to multiplicity in every concept in the theory of graphs when generalized to semigraphs. In this paper, we define a representing matrix of a semigraph [Formula: see text] and call it binomial incidence matrix of the semigraph [Formula: see text]. This matrix, which becomes the well-known incidence matrix when the semigraph is a graph, represents the semigraph uniquely, up to isomorphism. We characterize this matrix and derive some results on the rank of the matrix. We also show that a matrix derived from the binomial incidence matrix satisfies a result in graph theory which relates incidence matrix of a graph and adjacency matrix of its line graph. We extend the concept of “twin vertices” in the theory of graphs to semigraph theory, and characterize them. Finally, we derive a systematic approach to show that the binomial incidence matrix of any semigraph on [Formula: see text] vertices can be obtained from the incidence matrix of the complete graph [Formula: see text].

scholarly journals Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yajing Wang ◽  
Yubin Gao
Keyword(s):  
Graph Theory ◽  
Spectral Radius ◽  
Adjacency Matrix ◽  
Upper Bounds ◽  
Simple Graph ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Spectral Graph ◽  
Vertex Set

Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

An Algorithm for Determining the Position and Orientation of 3-D Objects from Images Using Spectral Graph Theory

2015 ◽  
Vol 770 ◽  
pp. 585-591
Author(s):  
Alexey Barinov ◽  
Aleksey Zakharov
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Spectral Decomposition ◽  
Spectral Graph Theory ◽  
Feature Points ◽  
Image Comparison ◽  
Spectral Graph ◽  
Position And Orientation ◽  
Weighted Adjacency Matrix

This paper describes an algorithm for computing the position and orientation of 3-D objects by comparing graphs. The graphs are based on feature points of the image. Comparison is performed by a spectral decomposition with obtaining eigenvectors of weighted adjacency matrix of the graph.

Comparative Study of the Daily Lifestyle of Patients with Meniere's Disease and Controls

2005 ◽  
Vol 114 (12) ◽  
pp. 927-933 ◽  
Author(s):  
Junichi Onuki ◽  
Masahiro Takahashi ◽  
Kyoko Odagiri ◽  
Ryoko Wada ◽  
Ririko Sato
Keyword(s):  
Hearing Loss ◽  
Low Frequency ◽  
Meniere’S Disease ◽  
Menière’S Disease ◽  
Behavior Patterns ◽  
Meniere's Disease ◽  
Ménière’S Disease ◽  
Menière's Disease ◽  
Control Groups ◽  
Ménière's Disease

Objectives: This study was performed to investigate the possibility that daily lifestyle may have a causal relationship with Meniere's disease. Methods: We conducted a questionnaire study of daily lifestyles among groups of patients with Meniere's disease and those with low-frequency hearing loss, and compared the results with those of control groups of local residents matched individually by gender and age. Results: The Meniere's disease group diverged most widely from the control groups in their behavior patterns. Significant divergence was especially indicated in their engrossed, self-inhibiting, and time-constrained behaviors. Although the low-frequency hearing loss group also exhibited similar tendencies toward engrossment and in their feeling pressed for time, their self-inhibiting behavior was less pronounced. There was no major difference between the endolymphatic hydrops patient groups and the control groups on other items in the study such as daily lifestyle, environmental stress, and means of relaxation. Conclusions: The results of the present study strongly suggest that there may be a link between an individual's specific behavior patterns and the onset of Meniere's disease.

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