Tag: Graph Theory

“The edges* of graphs* may… be imbued with directedness. A normal graph in which edges are undirected is said to be undirected. Otherwise, if arrows may be placed on one or both endpoints of the edges of a graph to indicate directedness, the graph is said to be directed. A directed graph in which each edge is given a unique direction (i.e., edges may not be bidirected and point in both directions at once) is called an oriented graph. A graph or directed graph together with a function which assigns a positive real number to each edge (i.e., an oriented edge-labeled graph) is known as a network.” (“Graph,” WolframMathWorld, retrieved 6/25/2020, including the picture).

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*What is the Gist of a “Graph” (Graph Theory)?

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Disclaimer:

I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. By definition, none of these posts address every aspect of a topic. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).

“Graphs* come in a wide variety of different sorts**. The most common type is graphs in which at most one edge* (i.e., either one edge or no edges) may connect any two vertices*. Such graphs are called simple graphs. If multiple edges are allowed between vertices, the graph is known as a multigraph***. Vertices are usually not allowed to be self-connected, but this restriction is sometimes relaxed to allow such “graph loops.” A graph that may contain multiple edges and graph loops is called a pseudograph” (“Graph,” WolframMathWorld, retrieved 6/25/2020, including the picture).

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*What is the Gist of a “Graph” (Graph Theory)?

**The Wikipedia page called “Graphs” contains a section describing many other types beyond those shown here (retrieved 6/25/2020).

***This is the general rule. However, according to “Multigraph,” from WolframMathWorld, there can be a lot of ambiguity in what is and isn’t required for a graph to be a multigraph.

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Disclaimer:

I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. By definition, none of these posts address every aspect of a topic. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).

“The word “graph” has (at least) two meanings in mathematics.

“In elementary mathematics, “graph” refers to a function graph or “graph of a function,” i.e., a plot.

“In a mathematician’s terminology, [especially in graph theory], a graph is a collection of points and lines connecting some (possibly empty) subset* of them. The points of a graph are most commonly known as graph vertices, but may also be called “nodes” or simply “points.” Similarly, the lines connecting the vertices of a graph are most commonly known as graph edges, but may also be called “arcs” or “lines.”” (“Graph,” WolframMathWorld, retrieved 6/25/2020)

Graphs seem to be used to show how different parts of a thing or things are connected with each other.

If interested in getting a better idea of what graphs are, a good starting point would be to read “Graph,” from WolframMathWorld, (retrieved 6/25/2020) and, after the other link, “Graph (discrete mathematics),” from Wikipedia (retrieved 6/25/2020), especially the section “Properties of graphs.”

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*What is the Gist of a “Subset”?

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Disclaimer:

I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. By definition, none of these posts address every aspect of a topic. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).