Topologically ordered nodes or layers of a topological order of a graph or of an isolated graph component.
Represents a component of this graph with an underlying lazy implementation.
Controls the properties of graph traversals with no specific root.
Represents a cycle in this graph listing the nodes and connecting edges on it with the following syntax:
Either a Right containing a valid topological order or a Left containing a node on a cycle.
Either a Right containing a valid topological order or a Left containing a node on a cycle.
Type alias for entries in degree maps returned by degreeSeqMap.
Type alias for entries in degree maps returned by degreeSeqMap.
Decreasing ordering of nodes with respect to their degree.
Base trait for graph Orderings.
Template for extended node visitors.
Properties and methods for creating modified properties in a fluent-interface manner.
Controls the properties of inner-edge graph traversals.
Controls the properties of inner-element graph traversals.
Controls the properties of inner-node down-up graph traversals.
Controls the properties of inner-node graph traversals.
Represents a topological sort layer.
Layers of a topological order of a graph or of an isolated graph component.
The result of a topological sort in the layered view.
The result of a topological sort in the layered view.
Ordering for the path dependent type NodeT.
Controls the properties of outer-edge graph traversals.
Controls the properties of outer-element graph traversals.
Controls the properties of outer-node down-up graph traversals.
Controls the properties of outer-node graph traversals.
Represents a path in this graph where
A Builder for valid paths in this graph.
Properties controlling traversals.
Properties controlling the scope of traversals.
A traversable topological order of nodes of a graph or of an isolated graph component.
Controls the properties of consecutive graph traversals starting at a root node.
The root-related methods Traverser will inherit.
Represents a walk in this graph where walk ::= node { edge node }
A walk/path contains at least one node followed by any number of
consecutive pairs of an edge and a node.
A Builder for valid walks in this graph.
Creates a new supergraph with an additional node, unless the node passed is already present.
Creates a new supergraph with an additional node, unless the node passed is already present.
the node to be added
the new supergraph containing all nodes and edges of this graph and node
additionally.
Creates a new supergraph with an additional edge, unless the edge passed is already present.
Creates a new supergraph with an additional edge, unless the edge passed is already present.
the edge to be added
the new supergraph containing all nodes and edges of this
graph plus edge.
Creates a new subgraph consisting of all nodes and edges of this graph except node
and those edges which node is incident with.
Creates a new subgraph consisting of all nodes and edges of this graph except node
and those edges which node is incident with.
the node to be removed.
the new subgraph of this graph after the "ripple" deletion of node.
Creates a new subgraph consisting of all nodes and edges of this graph except edge
and those nodes which are incident with edge and would become edge-less after deletion.
Creates a new subgraph consisting of all nodes and edges of this graph except edge
and those nodes which are incident with edge and would become edge-less after deletion.
the edge to be removed.
a new subgraph of this graph after the "ripple" deletion of edge from
this graph.
Creates a new subgraph consisting of all nodes and edges of this graph but edge.
Creates a new subgraph consisting of all nodes and edges of this graph but edge.
The node set remains unchanged.
the edge to be removed.
a new subgraph of this graph that contains all nodes and edges of this graph
except of edge.
Creates a new subgraph consisting of all nodes and edges of this graph but node
which is conditionally removed from this graph.
Creates a new subgraph consisting of all nodes and edges of this graph but node
which is conditionally removed from this graph. The removal only succeeds if the node
is not incident with any edges or it is only incident with hooks.
the node to be gently removed.
the new subgraph of this graph after the "gentle" deletion of node.
If node could not be deleted, the new graph is a copy of this graph.
Creates a ComponentTraverser responsible for invoking graph traversal methods that cover all components of this possibly disconnected graph.
Creates a ComponentTraverser responsible for invoking graph traversal methods that cover all components of this possibly disconnected graph.
The properties controlling subsequent traversals.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
The edge set of this Graph commonly referred to as E(G).
The edge set of this Graph commonly referred to as E(G).
Set of all contained edges.
The companion object of This.
The companion object of This.
Creates a InnerEdgeTraverser based on scala.collection.Traversable[EdgeT].
Creates a InnerEdgeTraverser based on scala.collection.Traversable[EdgeT].
The node where subsequent graph traversals start.
The properties controlling subsequent traversals.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
Creates a InnerElemTraverser based on scala.collection.Traversable[InnerElem].
Creates a InnerElemTraverser based on scala.collection.Traversable[InnerElem].
The node where subsequent graph traversals start.
The properties controlling subsequent traversals.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
Creates a InnerNodeDownUpTraverser based on scala.collection.Traversable[(Boolean, NodeT)]
where the Boolean parameter is true if the traversal takes
place in downward and false if it takes place in upward direction.
Creates a InnerNodeDownUpTraverser based on scala.collection.Traversable[(Boolean, NodeT)]
where the Boolean parameter is true if the traversal takes
place in downward and false if it takes place in upward direction.
The node where subsequent graph traversals start.
The properties controlling subsequent traversals. A kind different from DepthFirst will be ignored.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
Creates a InnerNodeTraverser based on scala.collection.Traversable[NodeT].
Creates a InnerNodeTraverser based on scala.collection.Traversable[NodeT].
The node where subsequent graph traversals start.
The properties controlling subsequent traversals.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
Instantiates a PathBuilder for this graph.
Instantiates a PathBuilder for this graph.
The node this path starts at.
Expected maximum number of nodes on this path.
Determines the edge to be selected between neighbor nodes if an edge is not supplied explicitly. This is only relevant in case of multigraphs.
Instantiates a WalkBuilder for this graph.
Instantiates a WalkBuilder for this graph.
The node this walk starts at.
Expected maximum number of nodes on this walk.
Determines the edge to be selected between neighbor nodes if an edge is not supplied explicitly. This is only relevant in case of multigraphs.
The node (vertex) set of this Graph commonly referred to as V(G).
The node (vertex) set of this Graph commonly referred to as V(G).
Set of all contained nodes.
Creates a OuterEdgeTraverser based on scala.collection.Traversable[E[N]].
Creates a OuterEdgeTraverser based on scala.collection.Traversable[E[N]].
The node where subsequent graph traversals start.
The properties controlling subsequent traversals.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
Creates a OuterElemTraverser based on scala.collection.Traversable[OuterElem].
Creates a OuterElemTraverser based on scala.collection.Traversable[OuterElem].
The node where subsequent graph traversals start.
The properties controlling subsequent traversals.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
Creates a OuterNodeDownUpTraverser based on scala.collection.Traversable[(Boolean, N)]
where the Boolean parameter is true if the traversal takes
place in downward and false if it takes place in upward direction.
Creates a OuterNodeDownUpTraverser based on scala.collection.Traversable[(Boolean, N)]
where the Boolean parameter is true if the traversal takes
place in downward and false if it takes place in upward direction.
The node where subsequent graph traversals start.
The properties controlling subsequent traversals. A kind different from DepthFirst will be ignored.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
Creates a OuterNodeTraverser based on scala.collection.Traversable[N].
Creates a OuterNodeTraverser based on scala.collection.Traversable[N].
The node where subsequent graph traversals start.
The properties controlling subsequent traversals.
Restricts subsequent graph traversals to visit only nodes holding this predicate.
Restricts subsequent graph traversals to walk only along edges that hold this predicate.
If a NodeOrdering or EdgeOrdering different from NoOrdering is supplied
neighbor nodes will visited during the traversal according to this ordering.
Creates a new supergraph with an additional node or edge, unless the node or edge passed is already present.
Creates a new supergraph with an additional node or edge, unless the node or edge passed is already present.
This method purely wraps +(node: N) respectively +(edge: E[N])
granting the same behavior.
the wrapped node or edge to be added; ; if elem is of type N,
the wrapped object is added to the node set otherwise to the edge set.
a new supergraph containing all nodes and edges of this graph
plus elem.
Creates a new subgraph consisting of all nodes and edges of this graph except elem.
Creates a new subgraph consisting of all nodes and edges of this graph except elem.
If elem is of type N, this method maps to -(node: N). Otherwise the edge is deleted
leaving the node set unchanged.
node or edge to be removed.
the new subgraph of this graph after the "ripple" deletion of the passed node or the simple deletion of the passed edge.
Creates a new subgraph consisting of all nodes and edges of this graph except elem.
Creates a new subgraph consisting of all nodes and edges of this graph except elem.
If elem is of type N, this method maps to -(node: N). Otherwise the edge is deleted
along with those incident nodes which would become edge-less after deletion.
node or edge to be removed.
a new subgraph of this graph after the "ripple" deletion of the passed node or edge.
Creates a new subgraph consisting of all nodes and edges of this graph but the elements
of coll which will be unconditionally removed.
Creates a new subgraph consisting of all nodes and edges of this graph but the elements
of coll which will be unconditionally removed. This operation differs from --
in that edges are deleted along with those incident nodes which would become isolated
after deletion.
the new subgraph containing all nodes and edges of this graph
after the "ripple" deletion of nodes and the simple deletion of edges in coll .
Ordering for the path dependent type EdgeT.
Decreasing ordering of integers.
The empty ElemOrdering.
Default edge filter letting path all edges (non-filter).
Default edge filter letting path all edges (non-filter).
An arbitrary edge between from and to that is available most efficiently.
An arbitrary edge between from and to that is available most efficiently.
Default node filter letting traverse all nodes (non-filter).
Default node filter letting traverse all nodes (non-filter).
Sorts all nodes of this graph by ordNode followed by all edges sorted by ordEdge
and concatinates their string representation nodeSeparator and edgeSeparator
respectively.
Sorts all nodes of this graph by ordNode followed by all edges sorted by ordEdge
and concatinates their string representation nodeSeparator and edgeSeparator
respectively.
to separate nodes by.
to separate edges by.
to separate nodes from edges by.
whether the node and edge set should be prefixed.
the node ordering defaulting to defaultNodeOrdering.
the edge ordering defaulting to defaultEdgeOrdering.
Prepares and calls plusPlus or minusMinus.
Prepares and calls plusPlus or minusMinus.
Checks whether a given node or edge is contained in this graph.
Checks whether a given node or edge is contained in this graph.
the node or edge the existence of which is to be checked
true if elem is contained in this graph
The degree set of this graph projected onto a map.
The degree set of this graph projected onto a map. The keys of the map are the degrees in decreasing order while the values are the number of inner nodes having the degree of the corresponding key.
The degree sequence of this graph projected onto a sequence of tuples.
The degree sequence of this graph projected onto a sequence of tuples. The first elements of the tuples are the degrees in non-increasing order while the second elements are the corresponding inner nodes.
The degree set of this graph projected onto a map.
The degree set of this graph projected onto a map. The keys of the map are the degrees in decreasing order while the values are sets of the corresponding inner nodes.
The degree sequence of this graph, that is the non-increasing sequence of degrees over all nodes.
The degree sequence of this graph, that is the non-increasing sequence of degrees over all nodes.
The degree set of this graph, that is the decreasing set of unique degrees over all nodes.
The degree set of this graph, that is the decreasing set of unique degrees over all nodes. Same as degreeSeq without duplicates.
Graph instances are equal if their nodes and edges turned
to outer nodes and outer edges are equal.
Graph instances are equal if their nodes and edges turned
to outer nodes and outer edges are equal. Any TraversableOnce
instance may also be equal to this graph if its set representation
contains equalling outer nodes and outer edges. Thus the following
expressions hold:
Graph(1~2, 3) == List(1~2, 3) Graph(1~2, 3) == List(1, 2, 2, 3, 2~1)
The first test is false because of the failing nodes 1 and 2.
The second is true because of duplicate elimination and undirected edge equivalence.
Searches for an edge node equaling to outerEdge in this graph.
Searches for an edge node equaling to outerEdge in this graph.
the outer edge to search for in this graph.
Some of the inner edge found or None.
Searches for an inner node equaling to outerNode in this graph.
Searches for an inner node equaling to outerNode in this graph.
Some of the inner node found or None.
Finds a cycle in this graph in any of its components
and calls visitor for each inner element visited during the search.
Finds a cycle in this graph in any of its components
and calls visitor for each inner element visited during the search.
See componentTraverser for more control by means of FluentProperties.
Searches for an inner edge equaling to outerEdge in this graph
which must exist in this graph.
Searches for an inner edge equaling to outerEdge in this graph
which must exist in this graph.
the outer edge to search for in this graph.
the inner edge if found. Otherwise NoSuchElementException is thrown.
Searches for an inner node equaling to outerNode in this graph
which must exist in this graph.
Searches for an inner node equaling to outerNode in this graph
which must exist in this graph.
the outer node to search for in this graph.
the inner node if found. Otherwise NoSuchElementException is thrown.
Searches for an inner edge equaling to outerEdge in this graph.
Searches for an inner edge equaling to outerEdge in this graph.
the outer edge to search for in this graph.
the inner edge to return if outerEdge cannot be found.
the inner edge looked up or default if no inner edge
equaling to edge could be found.
Searches for an inner node equaling to outerNode in this graph.
Searches for an inner node equaling to outerNode in this graph.
the outer node to search for in this graph.
the inner node to return if outerNode is not contained.
The inner node looked up or default if no inner node
equaling to outerNode could be found.
The size - commonly referred to as ||G|| - of this graph equaling to the number of edges.
The size - commonly referred to as ||G|| - of this graph equaling to the number of edges.
Method size is reserved for the number of nodes and edges
because Graph is also SetLike with set elements being nodes or edges.
Provides a shortcut for predicates involving any graph element.
Provides a shortcut for predicates involving any graph element.
In order to compute a subgraph of this graph, the result of this method
may be passed to any graph-level method requiring a predicate such as
count, exists, filter, filterNot, forall etc. For instance
val g = Graph(2~>3, 3~>1, 5) g filter g.having(nodes = _ >= 2) // yields Graph(2, 3, 5, 2~>3)
The predicate that must hold for the nodes.
The predicate that must hold for the edges. If omitted, all edges
between nodes to be included by nodes will also be included.
A partial function combining the passed predicates.
Populates this graph with nodes and edges.
Populates this graph with nodes and edges.
The implementing class will typically have a constructor with the same parameters
which is invoked by from of the companion object.
The isolated (and optionally any other) outer nodes that the node set of this graph is to be populated with.
The outer edges that the edge set of this graph is to be populated with. Nodes being the end of any of these edges will be added to the node set.
Whether this graph has no cycle.
Whether this graph has no cycle.
Whether all nodes are pairwise adjacent.
Whether all nodes are pairwise adjacent.
true if this graph is complete, false if this graph contains any
independent nodes.
Whether this graph is connected if it is undirected or
weakly connected if it is directed.
Whether this graph is connected if it is undirected or
weakly connected if it is directed.
true if f is not equivalent to anyEdge.
true if f is not equivalent to anyEdge.
true if f is not equivalent to anyNode.
true if f is not equivalent to anyNode.
Whether this graph has at least one cycle in any of its components.
Whether this graph has at least one cycle in any of its components.
true if this graph has at most 1 node.
true if this graph has at most 1 node.
Iterates over all nodes and all edges.
Iterates over all nodes and all edges.
iterator containing all nodes and all edges
(Changed in version 2.8.0) Set.map now returns a Set, so it will discard duplicate values.
The degree of the node having the highest degree or 0 if
this graph is empty.
The degree of the node having the highest degree or 0 if
this graph is empty.
The degree of the node having the least degree or 0 if
this graph is empty.
The degree of the node having the least degree or 0 if
this graph is empty.
Implements the heart of -- calling the from factory method of the companion object.
Implements the heart of -- calling the from factory method of the companion object.
Note that this method must be reimplemented in each module
having its own factory methods such as constrained does.
Calculates the nodes and edges arguments to be passed to a factory method
when delNodes and delEdges are to be deleted by --.
Calculates the nodes and edges arguments to be passed to a factory method
when delNodes and delEdges are to be deleted by --.
Node predicate always returning false.
Node predicate always returning false.
true if this graph has at least 2 nodes.
true if this graph has at least 2 nodes.
The order - commonly referred to as |G| - of this graph equaling to the number of nodes.
The order - commonly referred to as |G| - of this graph equaling to the number of nodes.
Implements the heart of ++ calling the from factory method of the companion object.
Implements the heart of ++ calling the from factory method of the companion object.
Note that this method must be reimplemented in each module
having its own factory methods such as constrained does.
(Changed in version 2.9.0) The behavior of scanRight has changed. The previous behavior can be reproduced with scanRight.reverse.
Same as asSortedString but additionally prefixed and parenthesized by stringPrefix.
Same as asSortedString but additionally prefixed and parenthesized by stringPrefix.
Ensures sorted nodes/edges unless this Graph has more than 100 elements.
Ensures sorted nodes/edges unless this Graph has more than 100 elements.
See also asSortedString and toSortedString.
Sorts this graph topologically.
Sorts this graph topologically.
called for each inner node or inner edge visited during the sort.
See componentTraverser for more control by means of FluentProperties.
Sorts every isolated component of this graph topologically.
Sorts every isolated component of this graph topologically.
called for each inner node or inner edge visited during the sort.
See componentTraverser for more control by means of FluentProperties.
The total degree of this graph equaling to the sum
of the degrees over all nodes or 0 if this graph is empty.
The total degree of this graph equaling to the sum
of the degrees over all nodes or 0 if this graph is empty.
the degree function to apply
to the nodes defaulting to Degree. Non-default predefined
degree functions are InDegree and OutDegree.
selects nodes to be included by their degree.
(Changed in version 2.9.0) transpose throws an IllegalArgumentException if collections are not uniformly sized.
(graph: StringAdd).+(other)
(graph: (Param[Param[N, E], EI]) ⇒ Boolean).andThen(g)
(graph: (Param[Param[N, E], EI]) ⇒ Boolean).apply(v1)
(graph: (Param[Param[N, E], EI]) ⇒ Boolean).compose(g)
(graph: MonadOps[Param[N, E]]).filter(p)
(graph: MonadOps[Param[N, E]]).flatMap(f)
(graph: MonadOps[Param[N, E]]).map(f)
(graph: StringAdd).self
(graph: StringFormat).self
(graph: OuterNode[Graph[N, E]]).stringPrefix
(graph: OuterNode[Graph[N, E]]).toString()
(graph: (Param[Param[N, E], EI]) ⇒ Boolean).toString()
(graph: MonadOps[Param[N, E]]).withFilter(p)
(Since version 2.10.0) use fold instead
(graph: ArrowAssoc[Graph[N, E]]).x
(Since version 2.10.0) Use leftOfArrow instead
(graph: Ensuring[Graph[N, E]]).x
(Since version 2.10.0) Use resultOfEnsuring instead
The main trait for immutable graphs bundling the functionality of traits concerned with specific aspects.
the type of the nodes (vertices) in this graph.
the kind of the edges in this graph.