Populate a tree from vectors with BGL

I have three different vectors of objects that I need to make a tree structure from them. Let's assume we have vector <obj> parents, vector <obj> children, and vector <obj> leaves. Therefore, each member of vector <obj> children has several children that sits at the end of the tree as leaves, and has one parent that sits as parents. What I am using is defining Vertex properties and Edges properties as below, and then define a bidirectional graph:

struct VertexData
{
    std::string obj_name; // concatenation of labels
    std::string obj_class_num;
    int num;
    vector <int> segments_list;
    bool is_leaf=false;
};

struct EdgeData
{
    std::string edge_name;
    double confidence;
};

typedef boost::adjacency_list<boost::vecS, boost::vecS,
        boost::bidirectionalS,
        VertexData,
        boost::property<boost::edge_weight_t, double, EdgeData> > Graph;

Graph graph;

What I am doing currently, is looping through the vector <obj> leaves, for each member, I find the parent and make an edge. Then assign properties to the edge and vertices. But then for next leaf, I should check if already it has a parent in the tree or I should add a new vertex for its parent. Another thing that I tried, was looping through the vector <obj> children, and for each member try to make its leaves and parent. But I am not sure what is the correct way to do this. Here is a link: adding custom vertices to a boost graph that I try to do the same but with iterations.