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Furthermore, the longest path problem is solvable in polynomial time on any class of graphs with bounded treewidth or bounded clique-width, such as the distance-hereditary graphs. Finally, it is clearly NP-hard on all graph classes on which the Hamiltonian path problem is NP-hard, such as on split graphs , circle graphs , and planar graphs .
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
Many statistical and data processing systems have functions to convert between these two presentations, for instance the R programming language has several packages such as the tidyr package.
The latter may occur even if the distance in the other direction between the same two vertices is defined. In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path ...
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If a graph is both a split graph and an interval graph, then its complement is both a split graph and a comparability graph, and vice versa. The split comparability graphs, and therefore also the split interval graphs, can be characterized in terms of a set of three forbidden induced subgraphs. [7] The split cographs are exactly the threshold ...
The Hausdorff distance is the longest distance someone can be forced to travel by an adversary who chooses a point in one of the two sets, from where they then must travel to the other set. In other words, it is the greatest of all the distances from a point in one set to the closest point in the other set.
A log-log chart spanning more than one order of magnitude along both axes: Semi-log or log-log (non-linear) charts x position; y position; symbol/glyph; color; connections; Represents data as lines or series of points spanning large ranges on one or both axes; One or both axes are represented using a non-linear logarithmic scale; Streamgraph