Breadth First Search

In computer science, the Time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
Since in the worst case breadth-first search has to consider all paths to all possible nodes the time complexity of breadth-first search is O(|E| + |V|) where |V| and |E| is the cardinality of set of vertices and edges respectively.
The complexity is this since every vertex and every edge will be explored in the worst case.

Space complexity is a measure of the amount of working storage an algorithm needs. That means how much memory, in the worst case, is needed at any point in the algorithm.
Since all of the nodes of a level must be saved until their child nodes in the next level have been generated, the space complexity is proportional to the number of nodes at the deepest level.
The space complexity can also be expressed as O(|V|) where |V| is the cardinality of the set of vertices.
In the worst case scenario, the graph has a depth of 1 and all vertices must be stored.