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In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing multiple edges between the same ...
NodeXL integrates into Microsoft Excel 2007, 2010, 2013, 2016, 2019 and 365 and opens as a workbook with a variety of worksheets containing the elements of a graph structure such as edges and nodes. NodeXL can also import a variety of graph formats such as edgelists, adjacency matrices, GraphML , UCINet .dl, and Pajek .net.
A multigraph with multiple edges (red) and several loops (blue). Not all authors allow multigraphs to have loops. In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges [1]), that is, edges that have the same end nodes.
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
The definitions of incidence matrix apply to graphs with loops and multiple edges. The column of an oriented incidence matrix that corresponds to a loop is all zero, unless the graph is signed and the loop is negative; then the column is all zero except for ±2 in the row of its incident vertex.
Some CFG examples: (a) an if-then-else (b) a while loop (c) a natural loop with two exits, e.g. while with an if...break in the middle; non-structured but reducible (d) an irreducible CFG: a loop with two entry points, e.g. goto into a while or for loop A control-flow graph used by the Rust compiler to perform codegen.
The loop is: reinforcing if, after going around the loop, one ends up with the same result as the initial assumption. balancing if the result contradicts the initial assumption. Or to put it in other words: reinforcing loops have an even number of negative links (zero also is even, see example below) balancing loops have an odd number of ...