Exploring graph properties
==========================

In this recipe, I show how to generate a series of graph libraries and measure
some arbitrary (honestly, not sure what they mean!) graph properties with
``NetworkX``. Additionally, I show how to make single-bead representations.

.. testcode:: recipe1-test
    :hide:

    import logging
    import pathlib

    import matplotlib.pyplot as plt
    import networkx as nx
    import numpy as np

    import agx

    logger = logging.getLogger(__name__)

    # Define a working directory.
    wd = pathlib.Path.cwd() / "source"/ "recipes" / "recipe_1_output"


.. testcode:: recipe1-test

    # Define the node counts for five different libraries. These are the same
    # as those used in the tests.
    node_counts = [
        {
            agx.NodeType(type_id=0, num_connections=4): 2,
            agx.NodeType(type_id=1, num_connections=2): 4,
        },
        {
            agx.NodeType(type_id=0, num_connections=4): 3,
            agx.NodeType(type_id=1, num_connections=2): 3,
            agx.NodeType(type_id=2, num_connections=2): 3,
        },
        {
            agx.NodeType(type_id=0, num_connections=3): 4,
            agx.NodeType(type_id=1, num_connections=2): 6,
        },
        {agx.NodeType(type_id=0, num_connections=4): 5},
        {
            agx.NodeType(type_id=0, num_connections=3): 2,
            agx.NodeType(type_id=1, num_connections=2): 2,
            agx.NodeType(type_id=2, num_connections=1): 2,
        },
    ]

Now we can iterate through and collect properties and make the layouts.

.. testcode:: recipe1-test

    datas = {}
    layouts = {}
    for nc in node_counts:
        iterator = agx.TopologyIterator(node_counts=nc)
        datas[iterator.graph_type] = {}
        layouts[iterator.graph_type] = {}
        for tc in iterator.yield_graphs():
            nx_graph = tc.get_nx_graph()
            rd = nx.resistance_distance(nx_graph)
            mean_resistance_distance = np.mean(
                [j for i in rd for j in rd[i].values() if j != 0.0]
            )
            eccentricity_mean = np.mean(
                list(nx.eccentricity(nx_graph).values())
            )
            datas[iterator.graph_type][tc.idx] = {
                "eccentricity_mean": eccentricity_mean,
                "mean_resistance_distance": mean_resistance_distance,
            }
            layouts[iterator.graph_type][tc.idx]= tc.get_layout(
                layout_type="kamada",
                scale=10,
            )

In the script, I show the the plotting of these data to create:

.. image:: recipe_1_output/graph_properties.png

It seems there is a relationship between these two properties.

Below, I use ``moldoc`` to visualise some of these graphs, treating each node
as a ``carbon``, like so:

.. code-block:: python

    iterator = agx.TopologyIterator(
        node_counts={agx.NodeType(type_id=0, num_connections=4): 5},
    )
    vertices_by_id = {
        i.id: i.num_connections for i in iterator.vertex_prototypes
    }
    for tc in iterator.yield_graphs():
        if tc.idx != 0:
            continue

        layout = tc.get_layout(layout_type="kamada", scale=5)
        moldoc_display_molecule = molecule.Molecule(
            atoms=(
                molecule.Atom(
                    atomic_number=conn_color[vertices_by_id[idx]],
                    position=position,
                )
                for idx, position in layout.items()
            ),
            bonds=(
                molecule.Bond(
                    atom1_id=edge[0],
                    atom2_id=edge[1],
                    order=1,
                ) for edge in tc.vertex_map
            ),
        )

Graph of 2-4FG_4-2FG, idx = 1:

.. moldoc::

    import moldoc.molecule as molecule
    import networkx as nx
    import numpy as np

    import agx

    conn_color = {
        4: 6,
        3: 7,
        2: 8,
        1: 1,
    }

    iterator = agx.TopologyIterator(
        node_counts={
            agx.NodeType(type_id=0, num_connections=4): 2,
            agx.NodeType(type_id=1, num_connections=2): 4,
        },
    )
    vertices_by_id = {
        i.id: i.num_connections for i in iterator.vertex_prototypes
    }
    for tc in iterator.yield_graphs():
        if tc.idx != 1:
            continue

        layout = tc.get_layout(layout_type="kamada", scale=5)
        moldoc_display_molecule = molecule.Molecule(
            atoms=(
                molecule.Atom(
                    atomic_number=conn_color[vertices_by_id[idx]],
                    position=position,
                )
                for idx, position in layout.items()
            ),
            bonds=(
                molecule.Bond(
                    atom1_id=edge[0],
                    atom2_id=edge[1],
                    order=1,
                ) for edge in tc.vertex_map
            ),
        )

Graph of 3-4FG_6-2FG, idx = 2:

.. moldoc::

    import moldoc.molecule as molecule
    import networkx as nx
    import numpy as np

    import agx

    conn_color = {
        4: 6,
        3: 7,
        2: 8,
        1: 1,
    }

    iterator = agx.TopologyIterator(
        node_counts={
            agx.NodeType(type_id=0, num_connections=4): 3,
            agx.NodeType(type_id=1, num_connections=2): 3,
            agx.NodeType(type_id=2, num_connections=2): 3,
        },
    )
    vertices_by_id = {
        i.id: i.num_connections for i in iterator.vertex_prototypes
    }
    for tc in iterator.yield_graphs():
        if tc.idx != 2:
            continue

        layout = tc.get_layout(layout_type="kamada", scale=5)
        moldoc_display_molecule = molecule.Molecule(
            atoms=(
                molecule.Atom(
                    atomic_number=conn_color[vertices_by_id[idx]],
                    position=position,
                )
                for idx, position in layout.items()
            ),
            bonds=(
                molecule.Bond(
                    atom1_id=edge[0],
                    atom2_id=edge[1],
                    order=1,
                ) for edge in tc.vertex_map
            ),
        )

Graph of 4-3FG_6-2FG, idx = 3:

.. moldoc::

    import moldoc.molecule as molecule
    import networkx as nx
    import numpy as np

    import agx

    conn_color = {
        4: 6,
        3: 7,
        2: 8,
        1: 1,
    }

    iterator = agx.TopologyIterator(
        node_counts={
            agx.NodeType(type_id=0, num_connections=3): 4,
            agx.NodeType(type_id=1, num_connections=2): 6,
        },
    )
    vertices_by_id = {
        i.id: i.num_connections for i in iterator.vertex_prototypes
    }
    for tc in iterator.yield_graphs():
        if tc.idx != 3:
            continue

        layout = tc.get_layout(layout_type="kamada", scale=5)
        moldoc_display_molecule = molecule.Molecule(
            atoms=(
                molecule.Atom(
                    atomic_number=conn_color[vertices_by_id[idx]],
                    position=position,
                )
                for idx, position in layout.items()
            ),
            bonds=(
                molecule.Bond(
                    atom1_id=edge[0],
                    atom2_id=edge[1],
                    order=1,
                ) for edge in tc.vertex_map
            ),
        )

Graph of 5-4FG, idx = 2:

.. moldoc::

    import moldoc.molecule as molecule
    import networkx as nx
    import numpy as np

    import agx

    conn_color = {
        4: 6,
        3: 7,
        2: 8,
        1: 1,
    }

    iterator = agx.TopologyIterator(
        node_counts={agx.NodeType(type_id=0, num_connections=4): 5},
    )
    vertices_by_id = {
        i.id: i.num_connections for i in iterator.vertex_prototypes
    }
    for tc in iterator.yield_graphs():
        if tc.idx != 2:
            continue

        layout = tc.get_layout(layout_type="kamada", scale=5)
        moldoc_display_molecule = molecule.Molecule(
            atoms=(
                molecule.Atom(
                    atomic_number=conn_color[vertices_by_id[idx]],
                    position=position,
                )
                for idx, position in layout.items()
            ),
            bonds=(
                molecule.Bond(
                    atom1_id=edge[0],
                    atom2_id=edge[1],
                    order=1,
                ) for edge in tc.vertex_map
            ),
        )


Graph of 2-3FG_2-2FG_2-1FG, idx = 0:

.. moldoc::

    import moldoc.molecule as molecule
    import networkx as nx
    import numpy as np

    import agx

    conn_color = {
        4: 6,
        3: 7,
        2: 8,
        1: 1,
    }

    iterator = agx.TopologyIterator(
        node_counts={
            agx.NodeType(type_id=0, num_connections=3): 2,
            agx.NodeType(type_id=1, num_connections=2): 2,
            agx.NodeType(type_id=2, num_connections=1): 2,
        },
    )
    vertices_by_id = {
        i.id: i.num_connections for i in iterator.vertex_prototypes
    }
    for tc in iterator.yield_graphs():
        if tc.idx != 0:
            continue

        layout = tc.get_layout(layout_type="kamada", scale=5)
        moldoc_display_molecule = molecule.Molecule(
            atoms=(
                molecule.Atom(
                    atomic_number=conn_color[vertices_by_id[idx]],
                    position=position,
                )
                for idx, position in layout.items()
            ),
            bonds=(
                molecule.Bond(
                    atom1_id=edge[0],
                    atom2_id=edge[1],
                    order=1,
                ) for edge in tc.vertex_map
            ),
        )

.. raw:: html

    <a class="btn-download" href="../_static/recipes/recipe_1.py" download>⬇️ Download Python Script</a>