Undirected #202204112045 treats edges as non-directional. This means that the edge \((u, v)\) and the edge \((v, u)\) are the same edge. It also indicates that an undirected graph cannot have loop and cycle. It is useful to represent a sparse graph.
An undirected graph is connected if there is a path from every vertex to every other vertex. If a removal of a node will not undermine its connectivity, then the graph is biconnected#.
We can find the minimum #202207081445 in 202204112129# and 202204112118#. However, the solution for digraph appears to be more difficult.
Hamiltonian Cycle is a simple cycle in an 202204112129# that visits every vertex.
Euler Path, unlike 202205101149, doesn’t need to be a cycle by itself. As long as all edges in the #202204112129 are visited exactly once, the graph is an Euler Path. Like 202205101149, the graph needs to be connected. In the graph, there must be exactly two vertices that has an odd number of edges.
Euler Circuit is an #202204112129 where there is a cycle that visits every edge exactly once. It has two properties. First, every vertex has a even number of edges. Second, the undirected graph is connected.
A directed graph is strongly connected if there is a path from every vertex to every other vertex. It is weakly connected if the graph is connected with the edges (strip off the direction and treat it as an 202204112129).
Biconnectivity is an attribute of a connected #202204112129 where removal of a node will not disconnect the graph. We could say that an undirected graph is biconnected if it satisfies this condition.