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- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_300%3A_Mathematical_Ideas_Textbook_(Muranaka)/06%3A_Miscellaneous_Extra_Topics/6.04%3A_Graph_Theory/6.4.00%3A_Graph_TheorySome definitions are important to understand before delving into Graph Theory: (1) A graph is a picture of dots called vertices and lines called edges. (2) An edge that starts and ends at the same ver...Some definitions are important to understand before delving into Graph Theory: (1) A graph is a picture of dots called vertices and lines called edges. (2) An edge that starts and ends at the same vertex is called a loop. (3) If there are two or more edges directly connecting the same two vertices, then these edges are called multiple edges. (4) If there is a way to get from one vertex of a graph to all the other vertices of the graph, then the graph is connected, otherwise it is disconnected.
- https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/13%3A_Graph_Theory
- https://math.libretexts.org/Courses/Las_Positas_College/Math_for_Liberal_Arts/04%3A_Graph_Theory
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_and_Graph_Theory_(Guichard)/05%3A_Graph_TheoryThis textmap is stilll under construction. Please forgive us. David Guichard (Whitman College) Thumbnail: A drawing of a graph. (Public Domain; AzaToth via Wikipedia)
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_and_Graph_Theory_(Guichard)Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics.Graph theory is concerned with various types of networks, or really models of net...Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics.Graph theory is concerned with various types of networks, or really models of networks called graphs. These are not the graphs of analytic geometry, but what are often described as "points connected by lines''.
- https://math.libretexts.org/Courses/Florida_SouthWestern_State_College/MGF_1131%3A_Mathematics_in_Context__(FSW)/07%3A_Graph_Theory/7.01%3A_Basic_Graphs_and_Graphs_StructureThis section introduces graph theory, defining graphs, vertices, and edges, and distinguishing simple graphs from multigraphs. It explores vertex classification, degrees, and various graph types like ...This section introduces graph theory, defining graphs, vertices, and edges, and distinguishing simple graphs from multigraphs. It explores vertex classification, degrees, and various graph types like complete and isomorphic graphs. Key concepts include walks, trails, paths, and graph connectivity, with applications in real-world scenarios such as Page Rank and fraud detection.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_in_Society_(Lippman)/06%3A_Graph_Theory
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Book%3A_College_Mathematics_for_Everyday_Life_(Inigo_et_al)/06%3A_Graph_Theory/6.01%3A_Graph_TheorySome definitions are important to understand before delving into Graph Theory: (1) A graph is a picture of dots called vertices and lines called edges. (2) An edge that starts and ends at the same ver...Some definitions are important to understand before delving into Graph Theory: (1) A graph is a picture of dots called vertices and lines called edges. (2) An edge that starts and ends at the same vertex is called a loop. (3) If there are two or more edges directly connecting the same two vertices, then these edges are called multiple edges. (4) If there is a way to get from one vertex of a graph to all the other vertices of the graph, then the graph is connected, otherwise it is disconnected.
- https://math.libretexts.org/Courses/Florida_SouthWestern_State_College/MGF_1131%3A_Mathematics_in_Context__(FSW)/07%3A_Graph_Theory/7.02%3A_Euler_Circuits_and_Eulerization_of_GraphThis section covers Euler paths and circuits, key concepts in graph theory from the Konigsberg Bridge Problem. An Euler path visits every edge once with distinct starting and ending vertices, while an...This section covers Euler paths and circuits, key concepts in graph theory from the Konigsberg Bridge Problem. An Euler path visits every edge once with distinct starting and ending vertices, while an Euler circuit starts and ends at the same vertex. A graph can have these if it meets specific vertex degree conditions.
- https://math.libretexts.org/Courses/Florida_SouthWestern_State_College/MGF_1131%3A_Mathematics_in_Context__(FSW)/07%3A_Graph_Theory/7.04%3A_TreesThis section covers trees in graph theory, defining them as connected acyclic graphs and exploring their significance in applications like family trees and computer networks. It discusses spanning tre...This section covers trees in graph theory, defining them as connected acyclic graphs and exploring their significance in applications like family trees and computer networks. It discusses spanning trees, including methods for their construction, emphasizing Kruskal's algorithm for finding minimum spanning trees to minimize connection costs. Key characteristics of spanning trees are highlighted, including their cycle-free nature and connection of all vertices.
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/15%3A_Basics_of_Networks/15.02%3A_Terminologies_of_Graph_TheoryBefore moving on to actual dynamical network modeling, we need to cover some basics of graph theory, especially the definitions of technical terms used in this field. Let’s begin with something we have ...Before moving on to actual dynamical network modeling, we need to cover some basics of graph theory, especially the definitions of technical terms used in this field. Let’s begin with something we have already discussed above: A network (or graph) consists of a set of nodes (or vertices, actors) and a set of edges (or links, ties) that connect those nodes.
