ImplicitSurfaceNetwork-xj/shared_module/container/wrapper/relation_graph.hpp

#pragma once

#include <utility>
#include "compressed_vector_tuple.hpp"
#include "../../utils/pointer_wrapper.hpp"
#include "../../utils/type_list.hpp"

// a specialization of n-partite graph
// the graph consists of nodes of N types, each node can only be connected with previous type or next type to its type
// and the edges of the graph should not have any property (like weight or what else)
namespace detail::relation_graph
{
enum class edge_bidirection { to_prev, to_next };

template <typename Graph, size_t TypeIndex, edge_bidirection direction>
struct edge_iterator;

template <typename Graph, size_t TypeIndex>
struct node_proxy;

template <typename Graph, size_t TypeIndex>
struct node_container_proxy;

template <typename Graph, size_t TypeIndex, edge_bidirection direction>
struct edge_proxy {
private:
    friend struct edge_iterator<Graph, TypeIndex, direction>;
    using index_type = typename Graph::index_type;

    pointer_wrapper<Graph> m_graph_ptr{};
    index_type             m_edge_index{};

    static constexpr auto to_node_layer =
        direction == edge_bidirection::to_prev ? (TypeIndex) : ((TypeIndex + 1) % Graph::layer_count);

public:
    edge_proxy(pointer_wrapper<Graph> graph_ptr, index_type edge_index) : m_graph_ptr(graph_ptr), m_edge_index(edge_index) {}

    edge_proxy(Graph* graph_ptr, index_type edge_index) : m_graph_ptr(graph_ptr), m_edge_index(edge_index) {}

    auto to()
    {
        const auto to = std::get<TypeIndex>(m_graph_ptr->m_edges).template fetch<0>(m_edge_index).to;
        assert(to != Graph::invalid_index);
        return node_proxy<Graph, to_node_layer>(m_graph_ptr, static_cast<index_type>(to));
    }

    auto to() const
    {
        const auto to = std::get<TypeIndex>(m_graph_ptr->m_edges).template fetch<0>(m_edge_index).to;
        assert(to != Graph::invalid_index);
        return node_proxy<Graph, to_node_layer>(m_graph_ptr, static_cast<index_type>(to));
    }

    auto& property()
    {
        static_assert(Graph::template has_edge_property<TypeIndex>,
                      "called layer of relation graph does not have edge property.");
        auto& edges = std::get<TypeIndex>(m_graph_ptr->m_edges);
        return edges.template fetch<1>(m_edge_index >> 1);
    }

    auto& property() const
    {
        static_assert(Graph::template has_edge_property<TypeIndex>,
                      "called layer of relation graph does not have edge property.");
        auto& edges = std::get<TypeIndex>(m_graph_ptr->m_edges);
        return edges.template fetch<1>(m_edge_index >> 1);
    }
};

template <typename Graph, size_t TypeIndex, edge_bidirection direction>
struct edge_iterator {
private:
    using index_type                    = typename Graph::index_type;
    static constexpr auto invalid_index = Graph::invalid_index;

    pointer_wrapper<Graph> m_graph_ptr{};
    index_type             m_edge_index{};

public:
    using iterator_category = std::forward_iterator_tag;
    using value_type        = edge_proxy<Graph, TypeIndex, direction>;
    using difference_type   = std::ptrdiff_t;
    using pointer           = value_type*;
    using reference         = value_type;

    edge_iterator(pointer_wrapper<Graph> graph_ptr, index_type edge_index) : m_graph_ptr(graph_ptr), m_edge_index(edge_index) {}

    bool operator==(const edge_iterator& other) const
    {
        return m_graph_ptr == other.m_graph_ptr && m_edge_index == other.m_edge_index;
    }

    bool operator!=(const edge_iterator& other) const { return !(*this == other); }

    value_type operator*() const { return value_type(m_graph_ptr, m_edge_index); }

    value_type operator->() const { return value_type(m_graph_ptr, m_edge_index); }

    edge_iterator& operator++()
    {
        if (m_edge_index != invalid_index) {
            m_edge_index = std::get<TypeIndex>(m_graph_ptr->m_edges).template fetch<0>(m_edge_index).next;
        }
        return *this;
    }

    edge_iterator operator++(int)
    {
        edge_iterator tmp = *this;
        ++(*this);
        return tmp;
    }
};

template <typename Graph, size_t TypeIndex, edge_bidirection direction>
struct edge_range {
private:
    using index_type                    = typename Graph::index_type;
    static constexpr auto invalid_index = Graph::invalid_index;

    pointer_wrapper<Graph> m_graph_ptr{};
    index_type             m_edge_index{};

public:
    using iterator = edge_iterator<Graph, TypeIndex, direction>;

    edge_range(pointer_wrapper<Graph> graph_ptr, index_type edge_index) : m_graph_ptr(graph_ptr), m_edge_index(edge_index) {}

    bool empty() const { return begin() == end(); }

    iterator begin() { return iterator(m_graph_ptr, m_edge_index); }

    iterator end() { return iterator(m_graph_ptr, invalid_index); }

    iterator begin() const { return iterator(m_graph_ptr, m_edge_index); }

    iterator end() const { return iterator(m_graph_ptr, invalid_index); }
};

template <typename Graph, size_t TypeIndex>
struct node_proxy {
private:
    friend struct node_container_proxy<Graph, TypeIndex>;
    using index_type = typename Graph::index_type;

    pointer_wrapper<Graph> m_graph_ptr{};
    index_type             m_node_index{};

public:
    node_proxy(pointer_wrapper<Graph> graph_ptr, index_type node_index) : m_graph_ptr(graph_ptr), m_node_index(node_index) {}

    auto index() const { return m_node_index; }

    auto& property()
    {
        static_assert(Graph::template has_node_property<TypeIndex>,
                      "called layer of relation graph does not have node property.");
        return std::get<TypeIndex>(m_graph_ptr->m_nodes).template fetch<1>(m_node_index);
    }

    auto& property() const
    {
        static_assert(Graph::template has_node_property<TypeIndex>,
                      "called layer of relation graph does not have node property.");
        return std::get<TypeIndex>(m_graph_ptr->m_nodes).template fetch<1>(m_node_index);
    }

    template <edge_bidirection direction>
    auto edges()
    {
        constexpr auto edge_tuple_index = Graph::template edge_tuple_index_v<TypeIndex, direction>;
        const auto&    node             = std::get<TypeIndex>(m_graph_ptr->m_nodes).template fetch<0>(m_node_index);
        if constexpr (direction == edge_bidirection::to_prev)
            return edge_range<Graph, edge_tuple_index, direction>(m_graph_ptr, node.first_edge_to_prev);
        else if constexpr (direction == edge_bidirection::to_next)
            return edge_range<Graph, edge_tuple_index, direction>(m_graph_ptr, node.first_edge_to_next);
        else
            static_assert(false, "illegal edge direction.");
    }

    template <edge_bidirection direction>
    auto edges() const
    {
        constexpr auto edge_tuple_index = Graph::template edge_tuple_index_v<TypeIndex, direction>;
        const auto&    node             = std::get<TypeIndex>(m_graph_ptr->m_nodes).template fetch<0>(m_node_index);
        if constexpr (direction == edge_bidirection::to_prev)
            return edge_range<Graph, edge_tuple_index, direction>(m_graph_ptr, node.first_edge_to_prev);
        else if constexpr (direction == edge_bidirection::to_next)
            return edge_range<Graph, edge_tuple_index, direction>(m_graph_ptr, node.first_edge_to_next);
        else
            static_assert(false, "illegal edge direction.");
    }
};

template <typename Graph, size_t TypeIndex>
bool operator==(const node_proxy<Graph, TypeIndex>& lhs, const node_proxy<Graph, TypeIndex>& rhs)
{
    return lhs.m_graph_ptr == rhs.m_graph_ptr && lhs.m_node_index == rhs.m_node_index;
}

template <typename Graph, size_t TypeIndex>
struct node_iterator {
private:
    using index_type = typename Graph::index_type;

    pointer_wrapper<Graph> m_graph_ptr{};
    index_type             m_node_index{};

public:
    using iterator_category = std::random_access_iterator_tag;
    using value_type        = node_proxy<Graph, TypeIndex>;
    using difference_type   = std::ptrdiff_t;
    using pointer           = value_type*;
    using reference         = value_type;

    node_iterator(pointer_wrapper<Graph> graph_ptr, index_type node_index) : m_graph_ptr(graph_ptr), m_node_index(node_index) {}

    bool operator==(const node_iterator& other) const
    {
        return m_graph_ptr == other.m_graph_ptr && m_node_index == other.m_node_index;
    }

    bool operator!=(const node_iterator& other) const { return !(*this == other); }

    bool operator<(const node_iterator& other) const { return m_node_index < other.m_node_index; }

    bool operator<=(const node_iterator& other) const { return m_node_index <= other.m_node_index; }

    bool operator>(const node_iterator& other) const { return m_node_index > other.m_node_index; }

    bool operator>=(const node_iterator& other) const { return m_node_index >= other.m_node_index; }

    value_type operator*() { return value_type(m_graph_ptr, m_node_index); }

    value_type operator*() const { return value_type(m_graph_ptr, m_node_index); }

    // value_type operator->() { return value_type(m_graph_ptr, m_node_index); }

    // value_type operator->() const { return value_type(m_graph_ptr, m_node_index); }

    node_iterator& operator++()
    {
        ++m_node_index;
        return *this;
    }

    node_iterator operator++(int)
    {
        node_iterator tmp = *this;
        ++m_node_index;
        return tmp;
    }

    node_iterator& operator--()
    {
        --m_node_index;
        return *this;
    }

    node_iterator operator--(int)
    {
        node_iterator tmp = *this;
        --m_node_index;
        return tmp;
    }

    node_iterator& operator+=(difference_type n)
    {
        m_node_index += static_cast<index_type>(n);
        return *this;
    }

    node_iterator& operator-=(difference_type n)
    {
        m_node_index -= static_cast<index_type>(n);
        return *this;
    }

    node_iterator operator+(difference_type n) const
    {
        return node_iterator(m_graph_ptr, static_cast<index_type>(m_node_index + n));
    }

    node_iterator operator-(difference_type n) const
    {
        return node_iterator(m_graph_ptr, static_cast<index_type>(m_node_index - n));
    }

    difference_type operator-(const node_iterator& other) const
    {
        return static_cast<difference_type>(m_node_index) - static_cast<difference_type>(other.m_node_index);
    }

    value_type operator[](difference_type n) const
    {
        return value_type(m_graph_ptr, static_cast<index_type>(m_node_index + n));
    }
};

template <typename Graph, size_t TypeIndex>
struct node_container_proxy {
private:
    pointer_wrapper<Graph> m_graph_ptr{};

public:
    using iterator       = node_iterator<Graph, TypeIndex>;
    using const_iterator = node_iterator<Graph, TypeIndex>;
    using index_type     = typename Graph::index_type;

    node_container_proxy()                                       = default;
    ~node_container_proxy()                                      = default;
    node_container_proxy(const node_container_proxy&)            = default;
    node_container_proxy(node_container_proxy&&)                 = default;
    node_container_proxy& operator=(const node_container_proxy&) = default;
    node_container_proxy& operator=(node_container_proxy&&)      = default;

    node_container_proxy(const Graph* ptr) : m_graph_ptr(const_cast<Graph*>(ptr)) {}

    template <typename size_type>
    void reserve(size_type size)
    {
        static_assert(std::is_integral_v<size_type>);
        std::get<TypeIndex>(m_graph_ptr->m_nodes).reserve_all(static_cast<size_t>(size));
    }

    template <typename size_type>
    void resize(size_type size)
    {
        static_assert(std::is_integral_v<size_type>);
        std::get<TypeIndex>(m_graph_ptr->m_nodes).resize_all(static_cast<size_t>(size));
    }

    bool empty() const { return std::get<TypeIndex>(m_graph_ptr->m_nodes).empty(); }

    auto size() const { return std::get<TypeIndex>(m_graph_ptr->m_nodes).size(); }

    void clear() { return std::get<TypeIndex>(m_graph_ptr->m_nodes).clear_all(); }

    void shrink_to_fit() { return std::get<TypeIndex>(m_graph_ptr->m_nodes).shrink_to_fit_all(); }

    template <typename size_type>
    node_proxy<Graph, TypeIndex> operator[](size_type index)
    {
        static_assert(std::is_integral_v<size_type>);
        return node_proxy<Graph, TypeIndex>(m_graph_ptr, static_cast<index_type>(index));
    }

    template <typename size_type>
    node_proxy<Graph, TypeIndex> operator[](size_type index) const
    {
        static_assert(std::is_integral_v<size_type>);
        return node_proxy<Graph, TypeIndex>(m_graph_ptr, static_cast<index_type>(index));
    }

    iterator begin() { return iterator(m_graph_ptr, 0); }

    iterator end() { return iterator(m_graph_ptr, static_cast<index_type>(size())); }

    const_iterator begin() const { return const_iterator(m_graph_ptr, 0); }

    const_iterator end() const { return const_iterator(m_graph_ptr, static_cast<index_type>(size())); }

    template <typename container>
    void set_properties(container&& cont)
    {
        static_assert(Graph::template has_node_property<TypeIndex>,
                      "called layer of relation graph does not have node property.");
        resize(cont.size());
        std::get<TypeIndex>(m_graph_ptr->m_nodes).template raw<1>() = cont;
    }
};

template <typename Graph, size_t TypeIndex>
struct edge_container_proxy {
private:
    pointer_wrapper<Graph> m_graph_ptr{};

public:
    edge_container_proxy()                                       = default;
    ~edge_container_proxy()                                      = default;
    edge_container_proxy(const edge_container_proxy&)            = default;
    edge_container_proxy(edge_container_proxy&&)                 = default;
    edge_container_proxy& operator=(const edge_container_proxy&) = default;
    edge_container_proxy& operator=(edge_container_proxy&&)      = default;

    edge_container_proxy(const Graph* ptr) : m_graph_ptr(const_cast<Graph*>(ptr)) {}

    template <typename size_type>
    void reserve(size_type size)
    {
        static_assert(std::is_integral_v<size_type>);
        std::get<TypeIndex>(m_graph_ptr->m_edges).reserve_all(static_cast<size_t>(size));
    }

    template <typename size_type>
    void resize(size_type size)
    {
        static_assert(std::is_integral_v<size_type>);
        std::get<TypeIndex>(m_graph_ptr->m_edges).resize_all(static_cast<size_t>(size));
    }

    bool empty() const { return std::get<TypeIndex>(m_graph_ptr->m_edges).empty(); }

    auto size() const { return static_cast<typename Graph::size_type>(std::get<TypeIndex>(m_graph_ptr->m_edges).size()); }

    void clear() { std::get<TypeIndex>(m_graph_ptr->m_edges).clear_all(); }

    void shrink_to_fit() { std::get<TypeIndex>(m_graph_ptr->m_edges).shrink_to_fit_all(); }
};

template <typename IndexType>
struct node {
    static_assert(std::is_integral_v<IndexType>);

    node()                       = default;
    ~node()                      = default;
    node(const node&)            = default;
    node(node&&)                 = default;
    node& operator=(const node&) = default;
    node& operator=(node&&)      = default;

    node(IndexType first_edge_to_prev, IndexType first_edge_to_next)
        : first_edge_to_prev(first_edge_to_prev), first_edge_to_next(first_edge_to_next)
    {
    }

    IndexType first_edge_to_prev{std::numeric_limits<IndexType>::max()};
    IndexType first_edge_to_next{std::numeric_limits<IndexType>::max()};
};

template <typename IndexType>
struct edge {
    static_assert(std::is_integral_v<IndexType>);

    edge()                       = default;
    ~edge()                      = default;
    edge(const edge&)            = default;
    edge(edge&&)                 = default;
    edge& operator=(const edge&) = default;
    edge& operator=(edge&&)      = default;

    edge(IndexType to, IndexType next) : to(to), next(next) {}

    IndexType to{};
    IndexType next{std::numeric_limits<IndexType>::max()};
};

template <typename IndexType, typename NodePropertyTuple, typename EdgePropertyTuple>
class graph;

template <typename IndexType, typename... NodeProperties, typename... EdgeProperties>
class graph<IndexType, type_list<NodeProperties...>, type_list<EdgeProperties...>>
{
protected:
    static_assert(std::is_integral_v<IndexType>);
    static_assert(sizeof...(NodeProperties) == sizeof...(EdgeProperties));
    static constexpr auto invalid_index = std::numeric_limits<IndexType>::max();

    std::tuple<compressed_vector_tuple<node<IndexType>, NodeProperties>...> m_nodes{};
    // for i-th tuple: the edge of layer i+1 to layer i and layer i to layer i+1, with the property to the edges
    // here the i+1 is modeled by layer count n
    std::tuple<compressed_vector_tuple<edge<IndexType>, EdgeProperties>...> m_edges{};

    template <size_t from_type_index, edge_bidirection direction>
    static constexpr auto edge_tuple_index_v =
        (direction == edge_bidirection::to_prev)
            ? ((from_type_index - 1 + sizeof...(NodeProperties)) % (sizeof...(NodeProperties)))
            : from_type_index;

public:
    using index_type                    = IndexType;
    static constexpr size_t layer_count = sizeof...(NodeProperties);
    template <size_t TypeIndex>
    using node_property_type = element_type_t<TypeIndex, type_list<NodeProperties...>>;
    template <size_t TypeIndex>
    static constexpr auto has_node_property = !std::is_void_v<node_property_type<TypeIndex>>;
    template <size_t TypeIndex>
    using edge_property_type = element_type_t<TypeIndex, type_list<EdgeProperties...>>;
    template <size_t TypeIndex>
    static constexpr auto has_edge_property = !std::is_void_v<edge_property_type<TypeIndex>>;

    template <size_t TypeIndex>
    node_container_proxy<graph, TypeIndex> nodes()
    {
        static_assert(TypeIndex < sizeof...(NodeProperties));
        return node_container_proxy<graph, TypeIndex>{this};
    }

    template <size_t TypeIndex>
    node_container_proxy<graph, TypeIndex> nodes() const
    {
        static_assert(TypeIndex < sizeof...(NodeProperties));
        return node_container_proxy<graph, TypeIndex>{this};
    }

    template <size_t TypeIndex>
    edge_container_proxy<graph, TypeIndex> edges()
    {
        static_assert(TypeIndex < sizeof...(EdgeProperties));
        return edge_container_proxy<graph, TypeIndex>{this};
    }

    template <size_t TypeIndex>
    edge_container_proxy<graph, TypeIndex> edges() const
    {
        static_assert(TypeIndex < sizeof...(EdgeProperties));
        return edge_container_proxy<graph, TypeIndex>{this};
    }

    // add edge between node 'from' of layer 'type_index' to node 'to' of layer 'type_index + 1'
    template <size_t type_index, typename size_type>
    void add_edge_pair(size_type from, size_type to)
    {
        static_assert(std::is_integral_v<size_type>);
        static_assert(type_index < sizeof...(NodeProperties));

        add_edge<type_index, edge_bidirection::to_next>(from, to);
        add_edge<(type_index + 1) % layer_count, edge_bidirection::to_prev>(to, from);
    }

    // add edge between node 'from' of layer 'type_index' to node 'to' of layer 'type_index + 1'
    template <size_t type_index, typename size_type, typename... Args>
    auto add_edge_pair(size_type from, size_type to, Args&&... args) -> std::enable_if_t<(sizeof...(Args) > 0)>
    {
        static_assert(std::is_integral_v<size_type>);
        static_assert(type_index < sizeof...(NodeProperties));

        add_edge_pair<type_index, edge_bidirection::to_next>(from, to, std::forward<Args>(args)...);
        add_edge_pair<(type_index + 1) % layer_count, edge_bidirection::to_prev>(to, from, std::forward<Args>(args)...);
    }

    // resize nodes/edges by given graph, and copy the connection between nodes from given graph
    // CAUTION: the size of properties of edges are not set
    template <typename IndexType_, typename... NodeProperties_, typename... EdgeProperties_>
    void copy_structure(const graph<IndexType_, type_list<NodeProperties_...>, type_list<EdgeProperties_...>>& graph)
    {
        static_assert(sizeof...(NodeProperties) == sizeof...(NodeProperties_));
        copy_structure_impl(graph, std::index_sequence_for<NodeProperties...>{});
    }

private:
    template <size_t type_index, edge_bidirection direction, typename size_type>
    void add_edge(size_type from, size_type to)
    {
        constexpr auto edge_tuple_index = edge_tuple_index_v<type_index, direction>;
        auto&          nodes            = std::get<type_index>(m_nodes);
        auto&          edges            = std::get<edge_tuple_index>(m_edges);
        if constexpr (direction == edge_bidirection::to_prev) {
            auto& next           = nodes.template fetch<0>(from).first_edge_to_prev;
            auto  cur_edge_index = static_cast<index_type>(edges.size());
            edges.template emplace_back<0>(static_cast<index_type>(to), next);
            next = cur_edge_index;
        } else if constexpr (direction == edge_bidirection::to_next) {
            auto& next           = nodes.template fetch<0>(from).first_edge_to_next;
            auto  cur_edge_index = static_cast<index_type>(edges.size());
            edges.template emplace_back<0>(static_cast<index_type>(to), next);
            next = cur_edge_index;
        } else
            static_assert(false, "illegal edge direction.");
    }

    template <size_t type_index, edge_bidirection direction, typename size_type, typename... Args>
    auto add_edge(size_type from, size_type to, Args&&... args)
        -> std::enable_if_t<has_edge_property<edge_tuple_index_v<type_index, direction>> && (sizeof...(Args) > 0)>
    {
        constexpr auto edge_tuple_index = edge_tuple_index_v<type_index, direction>;
        auto&          nodes            = std::get<type_index>(m_nodes);
        auto&          edges            = std::get<edge_tuple_index>(m_edges);
        if constexpr (direction == edge_bidirection::to_prev) {
            auto& next           = nodes.template fetch<0>(from).first_edge_to_prev;
            auto  cur_edge_index = static_cast<index_type>(edges.size());
            edges.template emplace_back<0>(static_cast<index_type>(to), next);
            edges.template emplace_back<2>(std::forward<Args>(args)...);
            next = cur_edge_index;
        } else if constexpr (direction == edge_bidirection::to_next) {
            auto& next           = &nodes.template fetch<0>(from).first_edge_to_next;
            auto  cur_edge_index = static_cast<index_type>(edges.size());
            edges.template emplace_back<0>(static_cast<index_type>(to), next);
            edges.template emplace_back<2>(std::forward<Args>(args)...);
            next = cur_edge_index;
        } else
            static_assert(false, "illegal edge direction.");
    }

    template <typename IndexType_, typename... NodeProperties_, typename... EdgeProperties_, size_t... indices>
    void copy_structure_impl(const graph<IndexType_, type_list<NodeProperties_...>, type_list<EdgeProperties_...>>& graph,
                             std::index_sequence<indices...>)
    {
        (std::get<indices>(this->m_nodes).resize_all(std::get<indices>(graph.m_nodes).size()), ...);
        ((std::get<indices>(this->m_nodes).template raw<0>() = std::get<indices>(graph.m_nodes).template raw<0>()), ...);

        (std::get<indices>(this->m_edges).template resize<0>(std::get<indices>(graph.m_edges).size()), ...);
        ((std::get<indices>(this->m_edges).template raw<0>() = std::get<indices>(graph.m_edges).template raw<0>()), ...);
        ((resize_edge_property<indices>(std::get<indices>(graph.m_edges).size())), ...);
    }

    template <size_t TypeIndex>
    void resize_edge_property(size_t edge_size)
    {
        if constexpr (has_edge_property<TypeIndex>) {
            assert(edge_size % 2 == 0);
            std::get<TypeIndex>(this->m_edges).template resize<1>(edge_size >> 1);
        }
    }

    template <typename IndexType_, typename NodePropertyTuple_, typename EdgePropertyTuple_>
    friend class graph;

    template <typename Graph, size_t TypeIndex>
    friend struct node_proxy;
    template <typename Graph, size_t TypeIndex, edge_bidirection direction>
    friend struct edge_proxy;
    template <typename Graph, size_t TypeIndex, edge_bidirection direction>
    friend struct edge_iterator;
    template <typename Graph, size_t TypeIndex, edge_bidirection direction>
    friend struct edge_range;
    template <typename Graph, size_t TypeIndex>
    friend struct node_container_proxy;
    template <typename Graph, size_t TypeIndex>
    friend struct edge_container_proxy;
};

template <size_t rest_count, typename... voids>
struct empty_properties {
    using type = typename empty_properties<rest_count - 1, void, voids...>::type;
};

template <typename... voids>
struct empty_properties<0, voids...> {
    using type = type_list<voids...>;
};
} // namespace detail::relation_graph

using edge_bidirection = detail::relation_graph::edge_bidirection;

template <typename... node_properties>
using node_properties_t = type_list<node_properties...>;

template <typename... edge_properties>
using edge_properties_t = type_list<edge_properties...>;

template <size_t count>
using empty_properties_t = typename detail::relation_graph::empty_properties<count>::type;

template <typename index_type, typename node_properties_t, typename edge_properties_t>
using relation_graph = detail::relation_graph::graph<index_type, node_properties_t, edge_properties_t>;