o h'@sdZddlmZddlZgdZejdddddZejdddd d Zejdddd d Z ejdddd dZ ejdddddZ ejdddddZ ejddZ ejddZdS)z5Functions for finding and evaluating cuts in a graph.)chainN)boundary_expansion conductancecut_sizeedge_expansionmixing_expansionnode_expansionnormalized_cut_sizevolumeweight) edge_attrsc CsHtj||||dd}|rt|tj||||dd}tdd|DS)aReturns the size of the cut between two sets of nodes. A *cut* is a partition of the nodes of a graph into two sets. The *cut size* is the sum of the weights of the edges "between" the two sets of nodes. Parameters ---------- G : NetworkX graph S : collection A collection of nodes in `G`. T : collection A collection of nodes in `G`. If not specified, this is taken to be the set complement of `S`. weight : object Edge attribute key to use as weight. If not specified, edges have weight one. Returns ------- number Total weight of all edges from nodes in set `S` to nodes in set `T` (and, in the case of directed graphs, all edges from nodes in `T` to nodes in `S`). Examples -------- In the graph with two cliques joined by a single edges, the natural bipartition of the graph into two blocks, one for each clique, yields a cut of weight one:: >>> G = nx.barbell_graph(3, 0) >>> S = {0, 1, 2} >>> T = {3, 4, 5} >>> nx.cut_size(G, S, T) 1 Each parallel edge in a multigraph is counted when determining the cut size:: >>> G = nx.MultiGraph(["ab", "ab"]) >>> S = {"a"} >>> T = {"b"} >>> nx.cut_size(G, S, T) 2 Notes ----- In a multigraph, the cut size is the total weight of edges including multiplicity. )datadefaultcss|]\}}}|VqdSN).0uvr rrl/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/networkx/algorithms/cuts.py Rzcut_size..)nx edge_boundary is_directedrsum)GSTr edgesrrrrs9rcCs.|r|jn|j}tdd|||dDS)a|Returns the volume of a set of nodes. The *volume* of a set *S* is the sum of the (out-)degrees of nodes in *S* (taking into account parallel edges in multigraphs). [1] Parameters ---------- G : NetworkX graph S : collection A collection of nodes in `G`. weight : object Edge attribute key to use as weight. If not specified, edges have weight one. Returns ------- number The volume of the set of nodes represented by `S` in the graph `G`. See also -------- conductance cut_size edge_expansion edge_boundary normalized_cut_size References ---------- .. [1] David Gleich. *Hierarchical Directed Spectral Graph Partitioning*. css|]\}}|VqdSrr)rrdrrrr}szvolume..r )r out_degreedegreer)rrr r#rrrr Us'r cCsX|dur t|t|}t||||d}t|||d}t|||d}|d|d|S)aReturns the normalized size of the cut between two sets of nodes. The *normalized cut size* is the cut size times the sum of the reciprocal sizes of the volumes of the two sets. [1] Parameters ---------- G : NetworkX graph S : collection A collection of nodes in `G`. T : collection A collection of nodes in `G`. weight : object Edge attribute key to use as weight. If not specified, edges have weight one. Returns ------- number The normalized cut size between the two sets `S` and `T`. Notes ----- In a multigraph, the cut size is the total weight of edges including multiplicity. See also -------- conductance cut_size edge_expansion volume References ---------- .. [1] David Gleich. *Hierarchical Directed Spectral Graph Partitioning*. Nrr r!r )setrr rrrr num_cut_edgesvolume_Svolume_Trrrr s -r cCsR|dur t|t|}t||||d}t|||d}t|||d}|t||S)apReturns the conductance of two sets of nodes. The *conductance* is the quotient of the cut size and the smaller of the volumes of the two sets. [1] Parameters ---------- G : NetworkX graph S : collection A collection of nodes in `G`. T : collection A collection of nodes in `G`. weight : object Edge attribute key to use as weight. If not specified, edges have weight one. Returns ------- number The conductance between the two sets `S` and `T`. See also -------- cut_size edge_expansion normalized_cut_size volume References ---------- .. [1] David Gleich. *Hierarchical Directed Spectral Graph Partitioning*. Nr!)r%rr minr&rrrrs (rcCs>|dur t|t|}t||||d}|tt|t|S)aReturns the edge expansion between two node sets. The *edge expansion* is the quotient of the cut size and the smaller of the cardinalities of the two sets. [1] Parameters ---------- G : NetworkX graph S : collection A collection of nodes in `G`. T : collection A collection of nodes in `G`. weight : object Edge attribute key to use as weight. If not specified, edges have weight one. Returns ------- number The edge expansion between the two sets `S` and `T`. See also -------- boundary_expansion mixing_expansion node_expansion References ---------- .. [1] Fan Chung. *Spectral Graph Theory*. (CBMS Regional Conference Series in Mathematics, No. 92), American Mathematical Society, 1997, ISBN 0-8218-0315-8 Nr$)r%rr*len)rrrr r'rrrrs)rcCs$t||||d}|}|d|S)usReturns the mixing expansion between two node sets. The *mixing expansion* is the quotient of the cut size and twice the number of edges in the graph. [1] Parameters ---------- G : NetworkX graph S : collection A collection of nodes in `G`. T : collection A collection of nodes in `G`. weight : object Edge attribute key to use as weight. If not specified, edges have weight one. Returns ------- number The mixing expansion between the two sets `S` and `T`. See also -------- boundary_expansion edge_expansion node_expansion References ---------- .. [1] Vadhan, Salil P. "Pseudorandomness." *Foundations and Trends in Theoretical Computer Science* 7.1–3 (2011): 1–336. r$)rnumber_of_edges)rrrr r'num_total_edgesrrrrs) rcs,ttfdd|D}t|t|S)uReturns the node expansion of the set `S`. The *node expansion* is the quotient of the size of the node boundary of *S* and the cardinality of *S*. [1] Parameters ---------- G : NetworkX graph S : collection A collection of nodes in `G`. Returns ------- number The node expansion of the set `S`. See also -------- boundary_expansion edge_expansion mixing_expansion References ---------- .. [1] Vadhan, Salil P. "Pseudorandomness." *Foundations and Trends in Theoretical Computer Science* 7.1–3 (2011): 1–336. c3s|]}|VqdSr) neighbors)rrrrrrfrz!node_expansion..)r%r from_iterabler+)rr neighborhoodrr0rrDs"rcCstt||t|S)uReturns the boundary expansion of the set `S`. The *boundary expansion* is the quotient of the size of the node boundary and the cardinality of *S*. [1] Parameters ---------- G : NetworkX graph S : collection A collection of nodes in `G`. Returns ------- number The boundary expansion of the set `S`. See also -------- edge_expansion mixing_expansion node_expansion References ---------- .. [1] Vadhan, Salil P. "Pseudorandomness." *Foundations and Trends in Theoretical Computer Science* 7.1–3 (2011): 1–336. )r+r node_boundary)rrrrrrls"r)NNr)__doc__ itertoolsrnetworkxr__all__ _dispatchablerr r rrrrrrrrrs(    >  *  4  /  . / '