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Trivial Graph Format
Trivial Graph Format (TGF) is a simple text-based adjacency list file format for describing graphs, widely used because of its simplicity. Format The format consists of a list of node definitions, which map node IDs to labels, followed by a list of edges, which specify node pairs and an optional edge label. Because of its lack of standardization, the format has many variations. For instance, some implementations of the format require the node IDs to be integers, while others allow more general alphanumeric identifiers. Each node definition is a single line of text starting with the node ID, separated by a space from its label. The node definitions are separated from the edge definitions by a line containing the "#" character. Each edge definition is another line of text, starting with the two IDs for the endpoints of the edge separated by a space. If the edge has a label, it appears on the same line after the endpoint IDs. The graph may be interpreted as a directed or undirected g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjacency List
In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph. This is one of several commonly used representations of graphs for use in computer programs. Implementation details An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first class objects, and in what kinds of objects are used to represent the vertices and edges. * An implementation suggested by Guido van Rossum uses a hash table to associate each vertex in a graph with an array of adjacent vertices. In this repre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex (graph Theory)
In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another. From the point of view of graph theory, vertices are treated as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices. A vertex ''w'' is said to be ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
