How do you find undirected vertices on a graph?
Two vertices are called adjacent if there is an edge between them. The degree of a vertex in an undirected graph is the number of edges associated with it. If a vertex has a loop, it contributes twice. In the above picture, the degree of vertex a is 2, and the degree of vertex c is 4.
How do you find an undirected triangle on a graph?
Given an Undirected simple graph, We need to find how many triangles it can have. For example below graph have 2 triangles in it. Let A[][] be adjacency matrix representation of graph. If we calculate A3, then the number of triangle in Undirected Graph is equal to trace(A3) / 6.
How to detect a cycle in an undirected graph?
union-find algorithm for cycle detection in undirected graphs. Approach: Run a DFS from every unvisited node. Depth First Traversal can be used to detect a cycle in a Graph. DFS for a connected graph produces a tree. There is a cycle in a graph only if there is a back edge present in the graph.
How to find a back edge in DFS?
A back edge is an edge that is joining a node to itself (self-loop) or one of its ancestor in the tree produced by DFS. To find the back edge to any of its ancestor keep a visited array and if there is a back edge to any visited node then there is a loop and return true.
When is the current edge of a graph a bridge?
The current edge ( v, t o) is a bridge if and only if none of the vertices t o and its descendants in the DFS traversal tree has a back-edge to vertex v or any of its ancestors. Indeed, this condition means that there is no other way from v to t o except for edge ( v, t o). Now we have to learn to check this fact for each vertex efficiently.
How to find all bridges in a graph?
Informally, the problem is formulated as follows: given a map of cities connected with roads, find all “important” roads, i.e. roads which, when removed, cause disappearance of a path between some pair of cities.