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A graph with 16 vertices and six bridges (highlighted in red) An undirected connected graph with no bridge edges. In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. [1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle.
A directed graph or digraph is a graph in ... The Königsberg Bridge problem ... rocs — a graph theory IDE; The Social Life of Routers — non-technical paper ...
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. [1] [2] Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, [3] industrial fieldbusses and computer networks.
A greedy embedding is an embedding of the given graph with the property that a failure of this type is impossible. Thus, it can be characterized as an embedding of the graph with the property that for every two nodes x and t, there exists a neighbor y of x such that d(x,t) > d(y,t), where d denotes the distance in the embedded space. [2]
In modern terms, one replaces each land masses with an abstract "vertex" or node, and each bridge with an abstract connection, an "edge", which only serves to record which pair of vertices (land masses) is connected by that bridge. The resulting mathematical structure is a graph. → →
The pre-computed distances between each node and the corresponding access node as well as the pairwise distances between transit nodes need to be stored in distance tables. In the grid-based implementation outlined above, this results in 16 bytes of storage that is required for each node of the road graph.
A node u is said to be active if x f (u) > 0 (i.e. the node u consumes flow), deficient if x f (u) < 0 (i.e. the node u produces flow), or conserving if x f (u) = 0. In flow networks, the source s is deficient, and the sink t is active. Pseudo-flows, feasible flows, and pre-flows are all examples of flow functions.