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A representation of adjacent vertices via hash tables leads to an amortized average time complexity of () to test adjacency of two given vertices and to remove an edge and an amortized average time complexity [7] of ( ()) to remove a given vertex x of degree (). The time complexity of the other operations and the asymptotic space ...
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 ...
If the edge has a label, it appears on the same line after the endpoint IDs. [3] The graph may be interpreted as a directed or undirected graph. For directed graphs, to specify the concept of bi-directionality in an edge, one may either specify two edges (forward and back) or differentiate the edge by means of a label.
The edge (,) is called the inverted edge of (,). Multiple edges , not allowed under the definition above, are two or more edges with both the same tail and the same head. In one more general sense of the term allowing multiple edges, [ 5 ] a directed graph is an ordered triple G = ( V , E , ϕ ) {\displaystyle G=(V,E,\phi )} comprising:
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 ...
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. [1] A key concept of the system is the graph (or edge or relationship).
The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases.. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation".
where the degree of a vertex counts the number of times an edge terminates at that vertex. In an undirected graph , this means that each loop increases the degree of a vertex by two. In a directed graph , the term degree may refer either to indegree (the number of incoming edges at each vertex) or outdegree (the number of outgoing edges at ...