Graph library - graph interface

I am trying to write simple graph lib in C++, BFS, DFS etc.. I want to create class GraphI which will represent any graph and will include necessary methods so my library could work. Could I add/remove/improve something from my code?

#pragma once
#include <algorithm>
#include "colors.h"
struct Vertex;
template < typename T >
class GraphI {

public:
    struct Vertex {
        Vertex( const T& k, color col = color::w, int c = -1 )
            : key( k )
            , color(col)
            , cost( c ) {}

        int getCost() const { return cost; }
        const T& getKey() const { return key; }
        T& getKey() { return key; }
        void setColor( color c ) { color = c; }
        color getColor() { return color; }

        int cost;
        color color;
        T key;
        bool operator<( const Vertex& v1 ) const {
            return key < v1.key;
        }
    };
    using Graph = std::map<Vertex, std::list<Vertex> >;
    GraphI() = default;
    virtual ~GraphI() = default;

    virtual void add_vertex( const T& vertex ) {
        // if exists then add else do nothing
        _graph[ vertex ] = {};
        ++_size;
    } 
    virtual void add_edge( const T& from,
                   const T& to,
                  int cost = -1 ) {
        // if vertices do NOT exist return
        auto it = _graph.find( from );
        if ( it == _graph.end() ) return;

        auto it2 = _graph.find( to );
        if ( it2 == _graph.end() ) return;



        auto& neighbours = it->second;
        auto it_exists = std::find_if( neighbours.begin(),
                        neighbours.end(),
                        [&to]( const Vertex& vertex ) { return vertex.getKey() == to; } );
        // if edge already exists
        if ( it_exists != neighbours.end() ) return;
        neighbours.emplace_back( Vertex(to, color::w, cost) );
    }
    virtual void remove_vertex( const T& vertex ) {
        _graph.erase( vertex );
        --_size;
        // remove all edges going TO vertex
        for ( auto& v : _graph ) { 
            auto it = std::find_if( v.second.begin(),
                        v.second.end(),
                        [&vertex]( const auto& v )
                        { return vertex == v.getKey(); } );
            // if vertex does NOT exist
            if ( it == v.second.end() ) return;
            v.second.erase( it );
        }

    }
    virtual void remove_edge( const T& from, const T& to ) {
        auto it = _graph.find( from );
        if ( it == _graph.end() ) return;

        auto &edges = it->second;
        auto it2 = std::find_if( edges.begin(), edges.end(),
                    [&]( const auto& vertex ) { return vertex.key == to; } );

        if ( it2 == edges.end() ) return;
        edges.erase( it2 );
    }

    const Graph& graph() const { return _graph; }
    unsigned size() const { return _size; }
private:
    Graph _graph;
    unsigned _size;
};