## Mercurial > repos > shellac > sam_consensus_v3

### view env/lib/python3.9/site-packages/networkx/algorithms/tree/recognition.py @ 0:4f3585e2f14b draft default tip

Find changesets by keywords (author, files, the commit message), revision
number or hash, or revset expression.

"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

author | shellac |
---|---|

date | Mon, 22 Mar 2021 18:12:50 +0000 |

parents | |

children |

line wrap: on

line source

""" Recognition Tests ================= A *forest* is an acyclic, undirected graph, and a *tree* is a connected forest. Depending on the subfield, there are various conventions for generalizing these definitions to directed graphs. In one convention, directed variants of forest and tree are defined in an identical manner, except that the direction of the edges is ignored. In effect, each directed edge is treated as a single undirected edge. Then, additional restrictions are imposed to define *branchings* and *arborescences*. In another convention, directed variants of forest and tree correspond to the previous convention's branchings and arborescences, respectively. Then two new terms, *polyforest* and *polytree*, are defined to correspond to the other convention's forest and tree. Summarizing:: +-----------------------------+ | Convention A | Convention B | +=============================+ | forest | polyforest | | tree | polytree | | branching | forest | | arborescence | tree | +-----------------------------+ Each convention has its reasons. The first convention emphasizes definitional similarity in that directed forests and trees are only concerned with acyclicity and do not have an in-degree constraint, just as their undirected counterparts do not. The second convention emphasizes functional similarity in the sense that the directed analog of a spanning tree is a spanning arborescence. That is, take any spanning tree and choose one node as the root. Then every edge is assigned a direction such there is a directed path from the root to every other node. The result is a spanning arborescence. NetworkX follows convention "A". Explicitly, these are: undirected forest An undirected graph with no undirected cycles. undirected tree A connected, undirected forest. directed forest A directed graph with no undirected cycles. Equivalently, the underlying graph structure (which ignores edge orientations) is an undirected forest. In convention B, this is known as a polyforest. directed tree A weakly connected, directed forest. Equivalently, the underlying graph structure (which ignores edge orientations) is an undirected tree. In convention B, this is known as a polytree. branching A directed forest with each node having, at most, one parent. So the maximum in-degree is equal to 1. In convention B, this is known as a forest. arborescence A directed tree with each node having, at most, one parent. So the maximum in-degree is equal to 1. In convention B, this is known as a tree. For trees and arborescences, the adjective "spanning" may be added to designate that the graph, when considered as a forest/branching, consists of a single tree/arborescence that includes all nodes in the graph. It is true, by definition, that every tree/arborescence is spanning with respect to the nodes that define the tree/arborescence and so, it might seem redundant to introduce the notion of "spanning". However, the nodes may represent a subset of nodes from a larger graph, and it is in this context that the term "spanning" becomes a useful notion. """ import networkx as nx __all__ = ["is_arborescence", "is_branching", "is_forest", "is_tree"] @nx.utils.not_implemented_for("undirected") def is_arborescence(G): """ Returns True if `G` is an arborescence. An arborescence is a directed tree with maximum in-degree equal to 1. Parameters ---------- G : graph The graph to test. Returns ------- b : bool A boolean that is True if `G` is an arborescence. Notes ----- In another convention, an arborescence is known as a *tree*. See Also -------- is_tree """ return is_tree(G) and max(d for n, d in G.in_degree()) <= 1 @nx.utils.not_implemented_for("undirected") def is_branching(G): """ Returns True if `G` is a branching. A branching is a directed forest with maximum in-degree equal to 1. Parameters ---------- G : directed graph The directed graph to test. Returns ------- b : bool A boolean that is True if `G` is a branching. Notes ----- In another convention, a branching is also known as a *forest*. See Also -------- is_forest """ return is_forest(G) and max(d for n, d in G.in_degree()) <= 1 def is_forest(G): """ Returns True if `G` is a forest. A forest is a graph with no undirected cycles. For directed graphs, `G` is a forest if the underlying graph is a forest. The underlying graph is obtained by treating each directed edge as a single undirected edge in a multigraph. Parameters ---------- G : graph The graph to test. Returns ------- b : bool A boolean that is True if `G` is a forest. Notes ----- In another convention, a directed forest is known as a *polyforest* and then *forest* corresponds to a *branching*. See Also -------- is_branching """ if len(G) == 0: raise nx.exception.NetworkXPointlessConcept("G has no nodes.") if G.is_directed(): components = (G.subgraph(c) for c in nx.weakly_connected_components(G)) else: components = (G.subgraph(c) for c in nx.connected_components(G)) return all(len(c) - 1 == c.number_of_edges() for c in components) def is_tree(G): """ Returns True if `G` is a tree. A tree is a connected graph with no undirected cycles. For directed graphs, `G` is a tree if the underlying graph is a tree. The underlying graph is obtained by treating each directed edge as a single undirected edge in a multigraph. Parameters ---------- G : graph The graph to test. Returns ------- b : bool A boolean that is True if `G` is a tree. Notes ----- In another convention, a directed tree is known as a *polytree* and then *tree* corresponds to an *arborescence*. See Also -------- is_arborescence """ if len(G) == 0: raise nx.exception.NetworkXPointlessConcept("G has no nodes.") if G.is_directed(): is_connected = nx.is_weakly_connected else: is_connected = nx.is_connected # A connected graph with no cycles has n-1 edges. return len(G) - 1 == G.number_of_edges() and is_connected(G)