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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

For a given node, the ego network corresponds to a sub-graph where only its adjacent neighbors and their mutual links are included. The respective ego networks of node 10 (A) and node 8 (B) exhibit similar structures, although their actual situation in the whole network differs significantly (node 10 is

On this graph, 2-3-6-5-2 is a cycle but not a circuit. 1-2-4-1 is a cycle and a circuit.

On this graph, the length of link (2,3) is 4 km, and the length of the path between 1 and 6 (1-4-5-6; 3 segments) is 15 km.