Algorithm for selecting all edges and vertices connected to one vertex

Here's how it ended up. I realized I needed to work entirely in terms of in-edges and out-edges:

// Graph-related types
typedef property < vertex_name_t, std::string > vertex_p;
typedef adjacency_list < vecS, vecS, bidirectionalS, vertex_p> graph_t;
typedef graph_t::vertex_descriptor vertex_t;
typedef std::set< graph_t::edge_descriptor > edge_set;

// Focussing algorithm
edge_set focus_on_vertex(graph_t& graph, const std::string& focus_vertex_name)
{
    const vertex_t focus_vertex = find_vertex_named(graph, focus_vertex_name);

    edge_set edges;
    collect_in_edges(graph, focus_vertex, edges);
    collect_out_edges(graph, focus_vertex, edges);

    return edges;
}

// Helpers
void collect_in_edges(const graph_t& graph, vertex_t vertex, edge_set& accumulator)
{
    typedef graph_t::in_edge_iterator edge_iterator;

    edge_iterator begin, end;
    boost::tie(begin, end) = in_edges(vertex, graph);
    for (edge_iterator i = begin; i != end; ++i)
    {
        if (accumulator.find(*i) == accumulator.end())
        {
            accumulator.insert(*i);
            collect_in_edges(graph, source(*i, graph), accumulator);
        }
    }
}

void collect_out_edges(const graph_t& graph, vertex_t vertex, edge_set& accumulator)
{
    typedef graph_t::out_edge_iterator edge_iterator;

    edge_iterator begin, end;
    boost::tie(begin, end) = out_edges(vertex, graph);
    for (edge_iterator i = begin; i != end; ++i)
    {
        if (accumulator.find(*i) == accumulator.end())
        {
            accumulator.insert(*i);
            collect_out_edges(graph, target(*i, graph), accumulator);
        }
    }
}

vertex_t find_vertex_named(const graph_t& graph, const std::string& name)
{
    graph_t::vertex_iterator begin, end;
    boost::tie(begin, end) = vertices(graph);
    for (graph_t::vertex_iterator i = begin; i != end; ++i)
    {
        if (get(vertex_name, graph, *i) == name)
            return *i;
    }

    return -1;
}

This also handles cycles before or after the vertex in question. My source dependency graph had cycles (shudder).

I made some attempts at generalizing collect_*_edges into a templated collect_edges, but I didn't have enough meta-programming debugging energy to spend on it.

Ok, so I'll translate and adapt my tutorial to your specific question. The documentation always assumes tons of "using namespace"; I won't use any so you know what is what. Let's begin :

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/astar_search.hpp>

First, define a Vertex and an Edge :

struct Vertex{
    string name; // or whatever, maybe nothing
};
struct Edge{
    // nothing, probably. Or a weight, a distance, a direction, ...
};

Create the type or your graph :

typedef boost::adjacency_list<  // adjacency_list is a template depending on :
    boost::listS,               //  The container used for egdes : here, std::list.
    boost::vecS,                //  The container used for vertices: here, std::vector.
    boost::directedS,           //  directed or undirected edges ?.
    Vertex,                     //  The type that describes a Vertex.
    Edge                        //  The type that describes an Edge
> MyGraph;

Now, you can use a shortcut to the type of the IDs of your Vertices and Edges :

typedef MyGraph::vertex_descriptor VertexID;
typedef MyGraph::edge_descriptor   EdgeID;

Instanciate your graph :

MyGraph graph;

Read your Graphviz data, and feed the graph :

for (each Vertex V){
    VertexID vID = boost::add_vertex(graph); // vID is the index of a new Vertex
    graph[vID].name = whatever;
}

Notice that graph[ a VertexID ] gives a Vertex, but graph[ an EdgeID ] gives an Edge. Here's how to add one :

EdgeID edge;
bool ok;
boost::tie(edge, ok) = boost::add_edge(u,v, graphe); // boost::add_edge gives a std::pair<EdgeID,bool>. It's complicated to write, so boost::tie does it for us. 
if (ok)  // make sure there wasn't any error (duplicates, maybe)
    graph[edge].member = whatever you know about this edge

So now you have your graph. You want to get the VertexID for Vertex "c". To keep it simple, let's use a linear search :

MyGraph::vertex_iterator vertexIt, vertexEnd;
boost::tie(vertexIt, vertexEnd) = vertices(graph);
for (; vertexIt != vertexEnd; ++vertexIt){
    VertexID vertexID = *vertexIt; // dereference vertexIt, get the ID
    Vertex & vertex = graph[vertexID];
    if (vertex.name == std::string("c")){} // Gotcha
}

And finally, to get the neighbours of a vertex :

MyGraph::adjacency_iterator neighbourIt, neighbourEnd;
boost::tie(neighbourIt, neighbourEnd) = adjacent_vertices( vertexIdOfc, graph );
for(){you got it I guess}

You can also get edges with

std::pair<out_edge_iterator, out_edge_iterator> out_edges(vertex_descriptor u, const adjacency_list& g)
std::pair<in_edge_iterator, in_edge_iterator> in_edges(vertex_descriptor v, const adjacency_list& g)
 // don't forget boost::tie !

So, for your real question :

• Find the ID of Vertex "c"
• Find in_edges recursively
• Find out_edges recursively

Example for in_edges (never compiled or tried, out of the top of my head):

void findParents(VertexID vID){
    MyGraph::inv_adjacency_iterator parentIt, ParentEnd;
    boost::tie(parentIt, ParentEnd) = inv_adjacent_vertices(vID, graph);
    for(;parentIt != parentEnd); ++parentIt){
        VertexID parentID = *parentIt;
        Vertex & parent = graph[parentID];
        add_edge_to_graphviz(vID, parentID); // or whatever
        findParents(parentID);
    }
}

For the other way around, just rename Parent into Children, and use adjacency_iterator / adjacent_vertices.