Introduction to graph theory

By K. Fraughnaugh. 1973

In graph theory, the term graph refers to a set of vertices and a set of edges. A vertex can be used to represent any object. Graphs may contain undirected or directed edges. An undirected edge is a set of two vertices. A directed edge is an ordered pair of two vertices where the edge goes from the first vertex to the second vertex. Graphs that contain directed edges are called directed graphs or digraphs.

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Citations in the corpus

Random graphs (2006, background): “thomas.bonald@telecom-paristech.fr January 2019 These lecture notes present various random graphs.”
An Innovative Approach Based on a Tree-Searching Algorithm for the Optimal Matching of Independently Optimum Sum and Difference Excitations (2008, background): “tree), each child being the root of a binary tree called a subtree [11], [12].”
Analysis of Biological Networks (2008, background): “A measure for the deviation from statistical independence is given by the mutual information [64,66].”
Comparison of descriptor spaces for chemical compound retrieval and classification (2006, methodology): “For these reasons, in order to generate all connected graph fragments, we developed an algorithm that was inspired by the recursive technique for generating all the spanning trees of a graph G [42].”
Global-stability problem for coupled systems of differential equations on networks (2010, background): “We refer the reader to [17,36] for detailed discussions.”
SEARCHING AND SWEEPING GRAPHS: A BRIEF SURVEY (2006, background): “For the most part, the graph theory terminology of [19] is employed.”
Geometric Graphs and Arrangements (2004, methodology): “A good introduction to many aspects of graph theory is the book of West [214], with its more then 500 references this book can serve as a starting point for deeper studies.”
Networks and epidemic models (2005, methodology): “The historical study of networks has its grounding in two disparate fields: social sciences (Leinhardt 1977; Scott 1991;Wasserman&Faust 1994) and graph theory (Harary 1969; Bollobás 1985; West 1996).”
Multifractal analysis of river networks: Sandbox approach (2004, background): “But river networks can be assimilated to tree-graphs (connected acyclic graphs), which are not dense when the number of nodes is finite [West, 1996]: this prevents the plane-filling dimension from being reached.”