add_edge(v1, v2, graph)- time complexity

Question

I need to build a graph and trying to decide how (for minimum time complexity).

From my understanding, there are two popular ways to store the graph's data: adjacency_list and adjacency_matrix .

The declaration of the graph is (undirected for example):

typedef adjacency_list <vecS, vecS, undirectedS> UGraph; // In case of adjacency_list

typedef adjacency_matrix<undirectedS> UGraph; // In case of adjacency_matrix

Both cases are using the function add_edge(v1,v2,UGraph) to add an edge between two vertices.

So my question is which model will make add_edge be less expensive — in time complexity manner and why?

I tried to read this explanation about time complexity of add_edge but this explanation is about OutEdgeList . So it got me confused.

Which model is less expensive for add_edge and why?

Answer 1

so my question is which data base will make add_edge be less expensive- in time complexity manner and why?

It's faster ( O(1) ) in matrix in comparison to adjacency list in which you need to traverse the whole list attached to particular vertex to add an edge.