{

typename graph_traits< Graph >::vertex_descriptor p;

using size_type = typename graph_traits< Graph >::degree_size_type;

auto delta = (std::numeric_limits< size_type >::max)();

typename graph_traits< Graph >::vertex_iterator i, iend;

for (boost::tie(i, iend) = vertices(g); i != iend; ++i)

if (degree(*i, g) < delta)

{

delta = degree(*i, g);

p = *i;

}

return std::make_pair(p, delta);

typename graph_traits< Graph >::vertex_descriptor u, OutputIterator result)

{

typename graph_traits< Graph >::adjacency_iterator ai, aend;

for (boost::tie(ai, aend) = adjacent_vertices(u, g); ai != aend; ++ai)

*result++ = *ai;

OutputIterator result)

{

for (; first != last; ++first)

neighbors(g, *first, result);

VertexListGraph& g, OutputIterator disconnecting_set)

{

using vertex_descriptor =

typename graph_traits< VertexListGraph >::vertex_descriptor;

using degree_size_type =

typename graph_traits< VertexListGraph >::degree_size_type;

using Color = color_traits< default_color_type >;

using edge_descriptor = typename adjacency_list_traits< vecS, vecS,

directedS >::edge_descriptor;

using FlowGraph = adjacency_list< vecS, vecS, directedS, no_property,

property< edge_capacity_t, degree_size_type,

property< edge_residual_capacity_t, degree_size_type,

property< edge_reverse_t, edge_descriptor > > > >;

vertex_descriptor u, v, p, k;

edge_descriptor e1, e2;

bool inserted;

typename graph_traits< VertexListGraph >::vertex_iterator vi, vi_end;

degree_size_type delta, alpha_star, alpha_S_k;

std::set< vertex_descriptor > S, neighbor_S;

std::vector< vertex_descriptor > S_star, nonneighbor_S;

std::vector< default_color_type > color(num_vertices(g));

std::vector< edge_descriptor > pred(num_vertices(g));

FlowGraph flow_g(num_vertices(g));

auto cap = get(edge_capacity, flow_g);

auto res_cap = get(edge_residual_capacity, flow_g);

auto rev_edge = get(edge_reverse, flow_g);

typename graph_traits< VertexListGraph >::edge_iterator ei, ei_end;

for (boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)

{

u = source(*ei, g), v = target(*ei, g);

boost::tie(e1, inserted) = add_edge(u, v, flow_g);

cap[e1] = 1;

boost::tie(e2, inserted) = add_edge(v, u, flow_g);

cap[e2] = 1;

rev_edge[e1] = e2;

rev_edge[e2] = e1;

}

boost::tie(p, delta) = min_degree_vertex(g);

S_star.push_back(p);

alpha_star = delta;

S.insert(p);

neighbor_S.insert(p);

neighbors(

g, S.begin(), S.end(), std::inserter(neighbor_S, neighbor_S.begin()));

std::set_difference(vertices(g).first, vertices(g).second,

neighbor_S.begin(), neighbor_S.end(),

std::back_inserter(nonneighbor_S));

while (!nonneighbor_S.empty())

{

k = nonneighbor_S.front();

alpha_S_k = edmonds_karp_max_flow(

flow_g, p, k, cap, res_cap, rev_edge, &color[0], &pred[0]);

if (alpha_S_k < alpha_star)

{

alpha_star = alpha_S_k;

S_star.clear();

for (boost::tie(vi, vi_end) = vertices(flow_g); vi != vi_end; ++vi)

if (color[*vi] != Color::white())

S_star.push_back(*vi);

}

S.insert(k);

neighbor_S.insert(k);

neighbors(g, k, std::inserter(neighbor_S, neighbor_S.begin()));

nonneighbor_S.clear();

std::set_difference(vertices(g).first, vertices(g).second,

neighbor_S.begin(), neighbor_S.end(),

std::back_inserter(nonneighbor_S));

}

std::vector< bool > in_S_star(num_vertices(g), false);

for (auto const& vertex : S_star.begin())

in_S_star[vertex] = true;

degree_size_type c = 0;

for (auto const& vertex : S_star.begin())

{

typename graph_traits< VertexListGraph >::out_edge_iterator ei, ei_end;

for (boost::tie(ei, ei_end) = out_edges(vertex, g); ei != ei_end; ++ei)

if (!in_S_star[target(*ei, g)])

{

*disconnecting_set++ = *ei;

++c;

}

}

return c;

{

using namespace boost;

GraphvizGraph g;

read_graphviz("figs/edge-connectivity.dot", g);

using edge_descriptor = graph_traits< GraphvizGraph >::edge_descriptor;

std::vector< edge_descriptor > disconnecting_set;

auto c = edge_connectivity(g, std::back_inserter(disconnecting_set));

std::cout << "The edge connectivity is " << c << "." << std::endl;

auto attr_map = get(vertex_attribute, g);

std::cout << "The disconnecting set is {";

for (auto const& edge : disconnecting_set)

std::cout << "(" << attr_map[source(edge, g)]["label"] << ","

<< attr_map[target(edge, g)]["label"] << ") ";

std::cout << "}." << std::endl;

return EXIT_SUCCESS;