pgmodeler | source data modeling tool designed for PostgreSQL | Database library

The documentation for the Graph concepts is conveniently here: https://www.boost.org/doc/libs/1_70_0/libs/graph/doc/graph_concepts.html

So - you never told us what algorithms you intend to use.

So let me pick an examples: BFS. The docs say it requires:

A directed or undirected graph. The graph type must be a model of Vertex List Graph and Incidence Graph.

Looking at your pre-existing data structures, it looks like you only cover the Vertex List use case easily.

The edges are implemented more as an Edge List. It's not possible to emulate Incidence Graph from Edge List without runtime or storage overhead (that's mathematics, nothing to do with library or code quality).

In reality, it's pretty likely that you omitted parts of your pre-existing data-structures that are relevant to the problem, as most algorithms will be highly sub-optimal on just Vertex+Edge lists.

In practice I suppose you Edge list might be organized like a classical adjacency list (e.g. ordering by source vertex, so you CAN have a O(log(n)) lookup by source vertex).

For the example below I'm assuming this is the case. Keep in mind we're only approaching the complexity guarantees from Incidence Graph Concept:

Complexity guarantees

The source(), target(), and out_edges() functions must all be constant time. The out_degree() function must be linear in the number of out-edges.

To actually meet these requirements, you will need to have dedicated storage of out-edges per vertex

So, let'st have a go: