Author : Matthias Dehmer
Publisher : CRC Press
Page : 528 pages
File Size : 28,37 MB
Release : 2014-10-27
Category : Computers
ISBN : 1466584521
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical technique
Author : Matthias Dehmer
Publisher : John Wiley & Sons
Page : 298 pages
File Size : 48,65 MB
Release : 2017-09-12
Category : Medical
ISBN : 3527339094
This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.
Author : Mark R.T. Dale
Publisher : Cambridge University Press
Page : 355 pages
File Size : 31,82 MB
Release : 2017-11-09
Category : Mathematics
ISBN : 110708931X
This book clearly describes the many applications of graph theory to ecological questions, providing instruction and encouragement to researchers.
Author : Courtney Brown
Publisher : SAGE
Page : 105 pages
File Size : 40,1 MB
Release : 2008
Category : Mathematics
ISBN : 1412941091
This book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated, algebraic statements of social and political phenomena.
Author : Ruggero Gramatica
Publisher :
Page : 428 pages
File Size : 16,37 MB
Release : 2015
Category :
ISBN :
I have shown how it is possible to fully capture the dynamical aspects of the phenomena under investigation by identifying clusters carrying influential information and tracking them over time. By computing graphbased statistics over such clusters I turn the evolution of textual information into a mathematically well-defined, multivariate time series, where each time series encodes the evolution of particular structural, topological and semantic properties of the set of concepts previously extracted and filtered. Eventually iv : : an autoregressive model with vectorial exogenous inputs is defined, which linearly mixes previous values of an index with the evolution of other time series induced by the semantic information in the graph. The methodology briefly described above concludes the contribution of my research work in the field of Complex Systems and it has been instrumental in successfully defining a graph-theoretical model for the study of drug repurposing [1 J and the construction of a framework for the analysis of financial and economic unstructured data (see chapter 6).
Author : Danail Bonchev
Publisher : Taylor & Francis
Page : 294 pages
File Size : 33,94 MB
Release : 1992
Category : Design
ISBN : 9780856265150
Building on the background of graph theory provided in the first volume of the series, presents a detailed examination of the role of graph theory in the study of chemical kinetics, reaction mechanisms, and quantitative structure-activity relations, in a manner useful to theoretical chemists. Among the topics are heterogeneous catalytic reactions, the classification and coding of chemical reaction mechanisms, the mechanist's description of chemical processes as it relates to aromaticity, and using operator networks to interpret evolutionary interrelations between chemical entities. Annotation copyright by Book News, Inc., Portland, OR
Author : Eric D. Kolaczyk
Publisher : Springer
Page : 214 pages
File Size : 50,42 MB
Release : 2014-05-22
Category : Computers
ISBN : 1493909835
Networks have permeated everyday life through everyday realities like the Internet, social networks, and viral marketing. As such, network analysis is an important growth area in the quantitative sciences, with roots in social network analysis going back to the 1930s and graph theory going back centuries. Measurement and analysis are integral components of network research. As a result, statistical methods play a critical role in network analysis. This book is the first of its kind in network research. It can be used as a stand-alone resource in which multiple R packages are used to illustrate how to conduct a wide range of network analyses, from basic manipulation and visualization, to summary and characterization, to modeling of network data. The central package is igraph, which provides extensive capabilities for studying network graphs in R. This text builds on Eric D. Kolaczyk’s book Statistical Analysis of Network Data (Springer, 2009).
Author : Mark R. T. Dale
Publisher : Cambridge University Press
Page : 250 pages
File Size : 22,29 MB
Release : 2021-04-15
Category : Nature
ISBN : 1108632971
Network thinking and network analysis are rapidly expanding features of ecological research. Network analysis of ecological systems include representations and modelling of the interactions in an ecosystem, in which species or factors are joined by pairwise connections. This book provides an overview of ecological network analysis including generating processes, the relationship between structure and dynamic function, and statistics and models for these networks. Starting with a general introduction to the composition of networks and their characteristics, it includes details on such topics as measures of network complexity, applications of spectral graph theory, how best to include indirect species interactions, and multilayer, multiplex and multilevel networks. Graduate students and researchers who want to develop and understand ecological networks in their research will find this volume inspiring and helpful. Detailed guidance to those already working in network ecology but looking for advice is also included.
Author : Béla Bollobás
Publisher : Courier Corporation
Page : 514 pages
File Size : 22,17 MB
Release : 2004-01-01
Category : Mathematics
ISBN : 0486435962
The ever-expanding field of extremal graph theory encompasses an array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume presents a concise yet comprehensive treatment, featuring complete proofs for almost all of its results and numerous exercises. 1978 edition.
Author : Sooyeong Kim
Publisher :
Page : 0 pages
File Size : 40,55 MB
Release : 2021
Category :
ISBN :
A fundamental mathematical approach uses graphs to understand networks representing objects with their interrelationships. This thesis is dedicated to qualitative and quantitative research through a bridge--the connections in a graph--with Gram mates arising in social networks; Fiedler vectors in networks; Kemeny's constant in road networks; and perfect state transfer in quantum spin networks. We use techniques from graph theory together with matrix theory--combinatorial matrix theory, algebraic graph theory, and spectral graph theory. Our main work is to examine two-mode networks retaining their information under the conversion approach in social networks. We characterize the relationship of two-mode networks (Gram mates) with the same single-mode networks via their singular values and vectors. So, we produce pairs of Gram mates that inform the retention of the information of two-mode networks. Furthermore, we provide Gram mates under mathematical restrictions. Our next goal is to inspect the robustness of the usage of Fiedler vectors in networks. One popular technique for detecting community structures is based on spectral bisection that uses Fiedler vectors for graph partitioning. We examine graphs where the partite sets resulting from spectral bisection are extremely different in size. We discuss pathological graphs where any choice of Fiedler vectors produces the bisection where one is a singleton and the other the rest. We furnish some classes of graphs that are potentially pathological. Our third task is to explain Braess' paradox in road networks. Kemeny's constant for a Markov chain can be used to measure the travel time of vehicles between two randomly chosen places. We present graphs where the insertion of an edge increases Kemeny's constant. We provide tools for identifying such an edge with examples of graphs, and produce families of graphs with such edges. Our goal of the final research is to switch interactions between qubits in a quantum spin network corresponding to a hypercube, in order for the manipulated spin network to become insensitive to external environments under perfect state transfer (PST). We investigate differences and similarities between hypercubes and the resulting graphs regarding the graph structure, PST, and the sensitivity of PST.
