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+"""Views of core data structures such as nested Mappings (e.g. dict-of-dicts).
+These ``Views`` often restrict element access, with either the entire view or
+layers of nested mappings being read-only.
+"""
+
+from collections.abc import Mapping
+
+__all__ = [
+    "AtlasView",
+    "AdjacencyView",
+    "MultiAdjacencyView",
+    "UnionAtlas",
+    "UnionAdjacency",
+    "UnionMultiInner",
+    "UnionMultiAdjacency",
+    "FilterAtlas",
+    "FilterAdjacency",
+    "FilterMultiInner",
+    "FilterMultiAdjacency",
+]
+
+
+class AtlasView(Mapping):
+    """An AtlasView is a Read-only Mapping of Mappings.
+
+    It is a View into a dict-of-dict data structure.
+    The inner level of dict is read-write. But the
+    outer level is read-only.
+
+    See Also
+    ========
+    AdjacencyView: View into dict-of-dict-of-dict
+    MultiAdjacencyView: View into dict-of-dict-of-dict-of-dict
+    """
+
+    __slots__ = ("_atlas",)
+
+    def __getstate__(self):
+        return {"_atlas": self._atlas}
+
+    def __setstate__(self, state):
+        self._atlas = state["_atlas"]
+
+    def __init__(self, d):
+        self._atlas = d
+
+    def __len__(self):
+        return len(self._atlas)
+
+    def __iter__(self):
+        return iter(self._atlas)
+
+    def __getitem__(self, key):
+        return self._atlas[key]
+
+    def copy(self):
+        return {n: self[n].copy() for n in self._atlas}
+
+    def __str__(self):
+        return str(self._atlas)  # {nbr: self[nbr] for nbr in self})
+
+    def __repr__(self):
+        return f"{self.__class__.__name__}({self._atlas!r})"
+
+
+class AdjacencyView(AtlasView):
+    """An AdjacencyView is a Read-only Map of Maps of Maps.
+
+    It is a View into a dict-of-dict-of-dict data structure.
+    The inner level of dict is read-write. But the
+    outer levels are read-only.
+
+    See Also
+    ========
+    AtlasView: View into dict-of-dict
+    MultiAdjacencyView: View into dict-of-dict-of-dict-of-dict
+    """
+
+    __slots__ = ()  # Still uses AtlasView slots names _atlas
+
+    def __getitem__(self, name):
+        return AtlasView(self._atlas[name])
+
+    def copy(self):
+        return {n: self[n].copy() for n in self._atlas}
+
+
+class MultiAdjacencyView(AdjacencyView):
+    """An MultiAdjacencyView is a Read-only Map of Maps of Maps of Maps.
+
+    It is a View into a dict-of-dict-of-dict-of-dict data structure.
+    The inner level of dict is read-write. But the
+    outer levels are read-only.
+
+    See Also
+    ========
+    AtlasView: View into dict-of-dict
+    AdjacencyView: View into dict-of-dict-of-dict
+    """
+
+    __slots__ = ()  # Still uses AtlasView slots names _atlas
+
+    def __getitem__(self, name):
+        return AdjacencyView(self._atlas[name])
+
+    def copy(self):
+        return {n: self[n].copy() for n in self._atlas}
+
+
+class UnionAtlas(Mapping):
+    """A read-only union of two atlases (dict-of-dict).
+
+    The two dict-of-dicts represent the inner dict of
+    an Adjacency:  `G.succ[node]` and `G.pred[node]`.
+    The inner level of dict of both hold attribute key:value
+    pairs and is read-write. But the outer level is read-only.
+
+    See Also
+    ========
+    UnionAdjacency: View into dict-of-dict-of-dict
+    UnionMultiAdjacency: View into dict-of-dict-of-dict-of-dict
+    """
+
+    __slots__ = ("_succ", "_pred")
+
+    def __getstate__(self):
+        return {"_succ": self._succ, "_pred": self._pred}
+
+    def __setstate__(self, state):
+        self._succ = state["_succ"]
+        self._pred = state["_pred"]
+
+    def __init__(self, succ, pred):
+        self._succ = succ
+        self._pred = pred
+
+    def __len__(self):
+        return len(self._succ.keys() | self._pred.keys())
+
+    def __iter__(self):
+        return iter(set(self._succ.keys()) | set(self._pred.keys()))
+
+    def __getitem__(self, key):
+        try:
+            return self._succ[key]
+        except KeyError:
+            return self._pred[key]
+
+    def copy(self):
+        result = {nbr: dd.copy() for nbr, dd in self._succ.items()}
+        for nbr, dd in self._pred.items():
+            if nbr in result:
+                result[nbr].update(dd)
+            else:
+                result[nbr] = dd.copy()
+        return result
+
+    def __str__(self):
+        return str({nbr: self[nbr] for nbr in self})
+
+    def __repr__(self):
+        return f"{self.__class__.__name__}({self._succ!r}, {self._pred!r})"
+
+
+class UnionAdjacency(Mapping):
+    """A read-only union of dict Adjacencies as a Map of Maps of Maps.
+
+    The two input dict-of-dict-of-dicts represent the union of
+    `G.succ` and `G.pred`. Return values are UnionAtlas
+    The inner level of dict is read-write. But the
+    middle and outer levels are read-only.
+
+    succ : a dict-of-dict-of-dict {node: nbrdict}
+    pred : a dict-of-dict-of-dict {node: nbrdict}
+    The keys for the two dicts should be the same
+
+    See Also
+    ========
+    UnionAtlas: View into dict-of-dict
+    UnionMultiAdjacency: View into dict-of-dict-of-dict-of-dict
+    """
+
+    __slots__ = ("_succ", "_pred")
+
+    def __getstate__(self):
+        return {"_succ": self._succ, "_pred": self._pred}
+
+    def __setstate__(self, state):
+        self._succ = state["_succ"]
+        self._pred = state["_pred"]
+
+    def __init__(self, succ, pred):
+        # keys must be the same for two input dicts
+        assert len(set(succ.keys()) ^ set(pred.keys())) == 0
+        self._succ = succ
+        self._pred = pred
+
+    def __len__(self):
+        return len(self._succ)  # length of each dict should be the same
+
+    def __iter__(self):
+        return iter(self._succ)
+
+    def __getitem__(self, nbr):
+        return UnionAtlas(self._succ[nbr], self._pred[nbr])
+
+    def copy(self):
+        return {n: self[n].copy() for n in self._succ}
+
+    def __str__(self):
+        return str({nbr: self[nbr] for nbr in self})
+
+    def __repr__(self):
+        return f"{self.__class__.__name__}({self._succ!r}, {self._pred!r})"
+
+
+class UnionMultiInner(UnionAtlas):
+    """A read-only union of two inner dicts of MultiAdjacencies.
+
+    The two input dict-of-dict-of-dicts represent the union of
+    `G.succ[node]` and `G.pred[node]` for MultiDiGraphs.
+    Return values are UnionAtlas.
+    The inner level of dict is read-write. But the outer levels are read-only.
+
+    See Also
+    ========
+    UnionAtlas: View into dict-of-dict
+    UnionAdjacency:  View into dict-of-dict-of-dict
+    UnionMultiAdjacency:  View into dict-of-dict-of-dict-of-dict
+    """
+
+    __slots__ = ()  # Still uses UnionAtlas slots names _succ, _pred
+
+    def __getitem__(self, node):
+        in_succ = node in self._succ
+        in_pred = node in self._pred
+        if in_succ:
+            if in_pred:
+                return UnionAtlas(self._succ[node], self._pred[node])
+            return UnionAtlas(self._succ[node], {})
+        return UnionAtlas({}, self._pred[node])
+
+    def copy(self):
+        nodes = set(self._succ.keys()) | set(self._pred.keys())
+        return {n: self[n].copy() for n in nodes}
+
+
+class UnionMultiAdjacency(UnionAdjacency):
+    """A read-only union of two dict MultiAdjacencies.
+
+    The two input dict-of-dict-of-dict-of-dicts represent the union of
+    `G.succ` and `G.pred` for MultiDiGraphs. Return values are UnionAdjacency.
+    The inner level of dict is read-write. But the outer levels are read-only.
+
+    See Also
+    ========
+    UnionAtlas:  View into dict-of-dict
+    UnionMultiInner:  View into dict-of-dict-of-dict
+    """
+
+    __slots__ = ()  # Still uses UnionAdjacency slots names _succ, _pred
+
+    def __getitem__(self, node):
+        return UnionMultiInner(self._succ[node], self._pred[node])
+
+
+class FilterAtlas(Mapping):  # nodedict, nbrdict, keydict
+    """A read-only Mapping of Mappings with filtering criteria for nodes.
+
+    It is a view into a dict-of-dict data structure, and it selects only
+    nodes that meet the criteria defined by ``NODE_OK``.
+
+    See Also
+    ========
+    FilterAdjacency
+    FilterMultiInner
+    FilterMultiAdjacency
+    """
+
+    def __init__(self, d, NODE_OK):
+        self._atlas = d
+        self.NODE_OK = NODE_OK
+
+    def __len__(self):
+        # check whether NODE_OK stores the number of nodes as `length`
+        # or the nodes themselves as a set `nodes`. If not, count the nodes.
+        if hasattr(self.NODE_OK, "length"):
+            return self.NODE_OK.length
+        if hasattr(self.NODE_OK, "nodes"):
+            return len(self.NODE_OK.nodes & self._atlas.keys())
+        return sum(1 for n in self._atlas if self.NODE_OK(n))
+
+    def __iter__(self):
+        try:  # check that NODE_OK has attr 'nodes'
+            node_ok_shorter = 2 * len(self.NODE_OK.nodes) < len(self._atlas)
+        except AttributeError:
+            node_ok_shorter = False
+        if node_ok_shorter:
+            return (n for n in self.NODE_OK.nodes if n in self._atlas)
+        return (n for n in self._atlas if self.NODE_OK(n))
+
+    def __getitem__(self, key):
+        if key in self._atlas and self.NODE_OK(key):
+            return self._atlas[key]
+        raise KeyError(f"Key {key} not found")
+
+    def __str__(self):
+        return str({nbr: self[nbr] for nbr in self})
+
+    def __repr__(self):
+        return f"{self.__class__.__name__}({self._atlas!r}, {self.NODE_OK!r})"
+
+
+class FilterAdjacency(Mapping):  # edgedict
+    """A read-only Mapping of Mappings with filtering criteria for nodes and edges.
+
+    It is a view into a dict-of-dict-of-dict data structure, and it selects nodes
+    and edges that satisfy specific criteria defined by ``NODE_OK`` and ``EDGE_OK``,
+    respectively.
+
+    See Also
+    ========
+    FilterAtlas
+    FilterMultiInner
+    FilterMultiAdjacency
+    """
+
+    def __init__(self, d, NODE_OK, EDGE_OK):
+        self._atlas = d
+        self.NODE_OK = NODE_OK
+        self.EDGE_OK = EDGE_OK
+
+    def __len__(self):
+        # check whether NODE_OK stores the number of nodes as `length`
+        # or the nodes themselves as a set `nodes`. If not, count the nodes.
+        if hasattr(self.NODE_OK, "length"):
+            return self.NODE_OK.length
+        if hasattr(self.NODE_OK, "nodes"):
+            return len(self.NODE_OK.nodes & self._atlas.keys())
+        return sum(1 for n in self._atlas if self.NODE_OK(n))
+
+    def __iter__(self):
+        try:  # check that NODE_OK has attr 'nodes'
+            node_ok_shorter = 2 * len(self.NODE_OK.nodes) < len(self._atlas)
+        except AttributeError:
+            node_ok_shorter = False
+        if node_ok_shorter:
+            return (n for n in self.NODE_OK.nodes if n in self._atlas)
+        return (n for n in self._atlas if self.NODE_OK(n))
+
+    def __getitem__(self, node):
+        if node in self._atlas and self.NODE_OK(node):
+
+            def new_node_ok(nbr):
+                return self.NODE_OK(nbr) and self.EDGE_OK(node, nbr)
+
+            return FilterAtlas(self._atlas[node], new_node_ok)
+        raise KeyError(f"Key {node} not found")
+
+    def __str__(self):
+        return str({nbr: self[nbr] for nbr in self})
+
+    def __repr__(self):
+        name = self.__class__.__name__
+        return f"{name}({self._atlas!r}, {self.NODE_OK!r}, {self.EDGE_OK!r})"
+
+
+class FilterMultiInner(FilterAdjacency):  # muliedge_seconddict
+    """A read-only Mapping of Mappings with filtering criteria for nodes and edges.
+
+    It is a view into a dict-of-dict-of-dict-of-dict data structure, and it selects nodes
+    and edges that meet specific criteria defined by ``NODE_OK`` and ``EDGE_OK``.
+
+    See Also
+    ========
+    FilterAtlas
+    FilterAdjacency
+    FilterMultiAdjacency
+    """
+
+    def __iter__(self):
+        try:  # check that NODE_OK has attr 'nodes'
+            node_ok_shorter = 2 * len(self.NODE_OK.nodes) < len(self._atlas)
+        except AttributeError:
+            node_ok_shorter = False
+        if node_ok_shorter:
+            my_nodes = (n for n in self.NODE_OK.nodes if n in self._atlas)
+        else:
+            my_nodes = (n for n in self._atlas if self.NODE_OK(n))
+        for n in my_nodes:
+            some_keys_ok = False
+            for key in self._atlas[n]:
+                if self.EDGE_OK(n, key):
+                    some_keys_ok = True
+                    break
+            if some_keys_ok is True:
+                yield n
+
+    def __getitem__(self, nbr):
+        if nbr in self._atlas and self.NODE_OK(nbr):
+
+            def new_node_ok(key):
+                return self.EDGE_OK(nbr, key)
+
+            return FilterAtlas(self._atlas[nbr], new_node_ok)
+        raise KeyError(f"Key {nbr} not found")
+
+
+class FilterMultiAdjacency(FilterAdjacency):  # multiedgedict
+    """A read-only Mapping of Mappings with filtering criteria
+    for nodes and edges.
+
+    It is a view into a dict-of-dict-of-dict-of-dict data structure,
+    and it selects nodes and edges that satisfy specific criteria
+    defined by ``NODE_OK`` and ``EDGE_OK``, respectively.
+
+    See Also
+    ========
+    FilterAtlas
+    FilterAdjacency
+    FilterMultiInner
+    """
+
+    def __getitem__(self, node):
+        if node in self._atlas and self.NODE_OK(node):
+
+            def edge_ok(nbr, key):
+                return self.NODE_OK(nbr) and self.EDGE_OK(node, nbr, key)
+
+            return FilterMultiInner(self._atlas[node], self.NODE_OK, edge_ok)
+        raise KeyError(f"Key {node} not found")