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An edge list is a data structure used to represent a graph as a list of its edges. An (unweighted) edge is defined by its start and end vertex, so each edge may be represented by two numbers. [1] The entire edge list may be represented as a two-column matrix. [2] [3] An edge list may be considered a variation on an adjacency list which is ...
Vertices are stored as records or objects, and every vertex stores a list of adjacent vertices. This data structure allows the storage of additional data on the vertices. Additional data can be stored if edges are also stored as objects, in which case each vertex stores its incident edges and each edge stores its incident vertices. Adjacency ...
The main alternative to the adjacency list is the adjacency matrix, a matrix whose rows and columns are indexed by vertices and whose cells contain a Boolean value that indicates whether an edge is present between the vertices corresponding to the row and column of the cell.
Decomposition, defined as partitioning the edge set of a graph (with as many vertices as necessary accompanying the edges of each part of the partition), has a wide variety of questions. Often, the problem is to decompose a graph into subgraphs isomorphic to a fixed graph; for instance, decomposing a complete graph into Hamiltonian cycles.
The standard relational algebra and relational calculus, and the SQL operations based on them, are unable to express directly all desirable operations on hierarchies. The nested set model is a solution to that problem. An alternative solution is the expression of the hierarchy as a parent-child relation. Joe Celko called this the adjacency list ...
The main alternative data structure, also in use for this application, is the adjacency list. [11] [12] The space needed to represent an adjacency matrix and the time needed to perform operations on them is dependent on the matrix representation chosen for the underlying matrix.
The order of an edge = (,) in a directed hypergraph is | | = (| |, | |): that is, the number of vertices in its tail followed by the number of vertices in its head. The definition above generalizes from a directed graph to a directed hypergraph by defining the head or tail of each edge as a set of vertices ( C ⊆ X {\displaystyle C\subseteq X ...
A sample DSM with 7 elements and 11 dependency marks. The design structure matrix (DSM; also referred to as dependency structure matrix, dependency structure method, dependency source matrix, problem solving matrix (PSM), incidence matrix, N 2 matrix, interaction matrix, dependency map or design precedence matrix) is a simple, compact and visual representation of a system or project in the ...