Compile a list of clusters that make up this graph. Ie: for a graph ((A, B)C, D); , set of all clusters is {(A,B), (A,B,C)}. Can optionally allow the trivial leaf clusters in the set as desired.

Combine two networks into a single network object by making the roots of each network the children of a new root node.

Compute the minimally sized subnetwork of a network such that the leaf set of the subnetwork is a subset of the original network's leaf set.

Generate all possible trees that can be derived from the given network by removing hybrid edges and creating copies with subtrees that start at each non-reticulation node.

Generate the dominant tree from a given network by retaining only the reticulation edges with the highest inheritance probability and removing all other reticulation edges.

Count the number of reticulation nodes in a network.

Validate standard binary constraints. - Tree/internal nodes: indegree=1 (except root with 0), outdegree=2 - Reticulation nodes: indegree=2, outdegree=1 - Leaves: outdegree=0

Detect bubble structures as parallel directed edges (same (src, dest)).

Sample one displayed tree by selecting, for each reticulation, a single incoming edge with probability proportional to its inheritance probability.

Contract an internal edge by merging its endpoints.

Return a copy of the network re-rooted at `new_root` by orienting edges away from the new root using undirected BFS levels. This preserves node/edge attributes; reticulation indegrees may change depending on topology.

Compute pairwise distances between leaves on the underlying undirected graph. If use_branch_lengths is True, sum edge lengths; otherwise, use unit weights.

Compute bridges and articulation points on the underlying undirected graph using Tarjan's algorithm.

Compute the transitive reduction of an acyclic network: remove edges (u,v) for which an alternate directed path u -> ... -> v exists.

Return the biconnected components ("blobs") of the underlying undirected graph.

Decompose a phylogenetic network into its biconnected components (blobs). Each blob is a maximal biconnected subgraph of the underlying undirected graph. Returns a list of Network objects, one per biconnected component, containing copies of the original nodes and directed edges. Node names are preserved but all objects are distinct from the original network.

Compute the level of a phylogenetic network. The level is the maximum number of reticulation nodes contained in any biconnected component ("blob") of the underlying undirected graph. Returns 0 for trees.

Estimate the number of displayed trees of a network. Computed as the product, over reticulation nodes, of their inbound edge counts (typically 2). For general networks, this is an upper bound when some choices may be incompatible; for level-1 networks this often matches the exact count.

Check whether a network is a tree (i.e., has no reticulation nodes).

Validate node times and branch lengths consistency across the network. For each edge (parent u -> child v), verify: - child_time - parent_time ≈ edge.length within tolerance. - child_time >= parent_time (monotonicity).

Compute the ancestor and descendant sets for each node in a network.

Compute a topological order of nodes in an acyclic network. Delegates to :pymeth:`Network.topological_order`.

Produce an acyclic copy by removing a small set of cycle-forming edges. Strategy 'greedy' removes the first encountered back edge per DFS pass until the graph is acyclic. This is not guaranteed minimal but is fast and effective for cleaning up accidental cycles.

Map each reticulation node to its inbound edges, sorted by gamma.

Construct the subnetwork induced by a set of leaf labels. The induced subnetwork is formed by taking the MRCA of the target leaves and retaining only those descendant branches that lead to at least one target leaf. Node/edge attributes (gamma, length) are copied where applicable.

Extract the topology from a newick string by removing branch lengths, inheritance probabilities, and other metadata. This function handles PhyloNet-style newick strings that may contain: - Branch lengths after single colons (:) - Inheritance probabilities after double colons (::) - Additional metadata after triple colons (:::) - Comments in square brackets [...]

Extract topology from all newick strings in a file.

Returns True, if net1 and net2 are topologically identical networks. Even if branch lengths are different, or node labels are different, networks can be isomorphic. ie-- all trees with 3 taxa are isomorphic. quartet trees have only a few different variations. Networks of any size, have infinitely many possible topologies. (A,B)C; is isomorphic with (D,E)F; (A,B),(C,D); is not isomorphic with ((A,B)C, D);

Hardwired cluster distance between two phylogenetic networks. The hardwired cluster of a node v is the set of all leaf labels reachable from v by following every directed edge. The distance is the cardinality of the symmetric difference of the two hardwired cluster sets: d_HC(N1, N2) = |HC(N1) triangle HC(N2)| When *normalize* is True the result is divided by |HC(N1) | HC(N2)|, yielding a value in [0, 1]. Reference --------- Huson, Rupp & Scornavacca. *Phylogenetic Networks: Concepts, Algorithms and Applications* (2010), Chapter 7.

Softwired cluster distance between two phylogenetic networks. The softwired cluster set of a network is the union of cluster sets across all of its displayed trees. The distance is the cardinality of the symmetric difference: d_SC(N1, N2) = |SC(N1) triangle SC(N2)| .. note:: This enumerates all 2^k displayed trees where k is the number of reticulations. For networks with many reticulations the cost is exponential. When *normalize* is True the result is divided by |SC(N1) | SC(N2)|, yielding a value in [0, 1]. Reference --------- Huson, Rupp & Scornavacca. *Phylogenetic Networks: Concepts, Algorithms and Applications* (2010), Chapter 7.

Mu-representation distance between two phylogenetic networks. For every node v in a network with leaf set X = {l_1, ..., l_n} the *mu-vector* is mu(v) = (m(v, l_1), ..., m(v, l_n)) where m(v, l_i) is the number of directed paths from v to leaf l_i. The *mu-representation* of a network is the multiset of mu-vectors over all nodes. The distance is the size of the multiset symmetric difference of the two mu-representations. This is a metric on the space of *reduced* phylogenetic networks (networks with no degree-2 tree nodes and no parallel edges). It is also referred to as the *topological distance for reduced networks*. For trees it reduces to the Robinson--Foulds distance. Both networks must share the same leaf label set. Reference --------- Cardona, Llabres, Rossello & Valiente. *Metrics for Phylogenetic Networks I: Generalizations of the Robinson-Foulds Metric*. IEEE/ACM Trans. Comput. Biol. Bioinformatics **6** (2009), 46--61.

Tripartition-based distance between two phylogenetic networks. For each tree node u with exactly two children c_1, c_2 the tripartition is (desc(c_1), desc(c_2), X \ (desc(c_1) | desc(c_2))) where X is the full leaf set. The distance is the cardinality of the symmetric difference of the tripartition sets: d_T(N1, N2) = |T(N1) triangle T(N2)| Reticulation nodes (in-degree >= 2) are excluded from tripartition generation. When *normalize* is True the result is divided by |T(N1) | T(N2)|, yielding a value in [0, 1]. Reference --------- Moret *et al.*; Huson, Rupp & Scornavacca. *Phylogenetic Networks: Concepts, Algorithms and Applications* (2010), Chapter 7.

Tree-based distance between two phylogenetic networks. Each network's set of unique displayed-tree topologies (identified by cluster representation) is computed. The distance is the cardinality of the symmetric difference: d_DT(N1, N2) = |DT(N1) triangle DT(N2)| .. note:: This enumerates all 2^k displayed trees per network. For networks with many reticulations the cost is exponential. When *normalize* is True the result is divided by |DT(N1) | DT(N2)|, yielding a value in [0, 1].

Robinson--Foulds distance between two phylogenetic trees or networks. For rooted trees the RF distance equals the cardinality of the symmetric difference of the non-trivial cluster sets (clusters of size >= 2 and < n, where n is the number of leaves). For networks the function uses hardwired clusters, which is the natural generalization of RF to DAGs. Both inputs must share the same leaf label set. When *normalize* is True the result is divided by |C(N1)| + |C(N2)| (the maximum possible RF for the given cluster counts), yielding a value in [0, 1]. Reference --------- Robinson & Foulds. *Comparison of Phylogenetic Trees*. Mathematical Biosciences **53** (1981), 131--147. Cardona, Llabres, Rossello & Valiente. *Metrics for Phylogenetic Networks I: Generalizations of the Robinson-Foulds Metric*. IEEE/ACM Trans. Comput. Biol. Bioinformatics **6** (2009), 46--61.

Average Path Distance (APD) between two phylogenetic networks. For each network a pairwise leaf distance matrix is computed by averaging the path lengths across all displayed trees (uniform weighting). The APD is the L1 norm of the difference between the two matrices: APD(N1, N2) = sum_{i<j} |D_N1(l_i,l_j) - D_N2(l_i,l_j)| When *normalize* is True the sum is divided by the number of leaf pairs C(n, 2). Branch lengths on every edge are required. .. note:: This enumerates all 2^k displayed trees per network. For networks with many reticulations the cost is exponential. Reference --------- Yakici, Ogilvie & Nakhleh. *Phylogenetic Network Dissimilarity Measures that Take Branch Lengths into Account*. RECOMB-CG 2022, LNCS 13234, pp. 86--102.

Weighted Average Path Distance (WAPD) between two networks. Identical to :func:`average_path_distance` except that the average over displayed trees is weighted by each tree's probability (the product of the gamma values of the kept reticulation edges). WAPD(N1, N2) = sum_{i<j} |WD_N1(l_i,l_j) - WD_N2(l_i,l_j)| When *normalize* is True the sum is divided by the number of leaf pairs C(n, 2). Branch lengths and gamma values on every reticulation edge are required. .. note:: This enumerates all 2^k displayed trees per network. For networks with many reticulations the cost is exponential. Reference --------- Yakici, Ogilvie & Nakhleh. *Phylogenetic Network Dissimilarity Measures that Take Branch Lengths into Account*. RECOMB-CG 2022, LNCS 13234, pp. 86--102.

Prints out an ascii art depiction of this Network object as a vertical tree/network with the root at the top and leaves at the bottom.

Prints a more detailed vertical ASCII art depiction of the Network with extended connecting lines between levels for wide trees.