Every edge appears twice in Adjacency List. Edge v-w will appear in v's adjacency and w's adjacency.
Connected Component
Find the Number of connected components in an undirected graph. (BFS/DFS/Union Find Can be used to do this)
In the Directed graph the equivalent Concept is Strongly Connected Component.(Kosarajus Algorithm)
Weighted Graph
Equal Weighted Graph
General Weighted Graph
Minimum Spanning Tree
The minimum spanning tree of a graph is unique if all m edge weights in the
graph are distinct. Otherwise the order in which Prim’s/Kruskal’s algorithm breaks
ties determines which minimum spanning tree is returned.