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A, B, C, and D graphs have respective diameters of 2, 3, 4, and 3. Adding a link on graph C between nodes 4 and 6 reduced the diameter by 1 (graph D).

The diameter of a graph is the length of the shortest path between the most distanced nodes. d measures the extent of a graph and the topological length between two nodes. The number of links (edges) between the furthest nodes (2 and 7) of the above graph is 4. Consequently,

On this graph, link (3,4) is an isthmus since removing the link creates two connected subgraphs. Link (4,5) is not an isthmus since removing the link does create two subgraphs, but one graph is composed of only one node (5).

By removing node 1 from graph A, we obtain graph B, which is connected. 1 is thus not an articulation node. If we remove node 4 from graph A, the result is an unconnected graph C where p=2 (two subgraphs). Node 4 is thus the only articulation node of graph

This graph is a tree having node 1 as a root.

Node 1 is the only root of this graph because every other node is part of a path originating from node 1.

For graph G constructed from graph X, the complementary graph for G is graph Y if the union of X and Y is equal to G.

Connectivity is dependent on the arrangement of links between nodes, including their direction. In the above figure, the two graphs are connected, but graph B is more connected than graph A since it has two circuits compared with only one for graph A.

A method in space syntax that considers edges as nodes and nodes as edges. In urban street networks, large avenues made of several segments become single nodes, while intersections with other avenues or streets become links (edges). This method is particularly useful for revealing hierarchical structures in a planar network.

A nodal region refers to a subgroup (tree) of nodes polarized by an independent node (whose largest flow link connects a smaller node) and a number of subordinate nodes (whose largest flow link connects a larger node). Single or multiple linkage analysis methods are used to reveal such regions by