Mercurial > repos > shellac > sam_consensus_v3
diff env/lib/python3.9/site-packages/networkx/algorithms/core.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/env/lib/python3.9/site-packages/networkx/algorithms/core.py Mon Mar 22 18:12:50 2021 +0000 @@ -0,0 +1,534 @@ +""" +Find the k-cores of a graph. + +The k-core is found by recursively pruning nodes with degrees less than k. + +See the following references for details: + +An O(m) Algorithm for Cores Decomposition of Networks +Vladimir Batagelj and Matjaz Zaversnik, 2003. +https://arxiv.org/abs/cs.DS/0310049 + +Generalized Cores +Vladimir Batagelj and Matjaz Zaversnik, 2002. +https://arxiv.org/pdf/cs/0202039 + +For directed graphs a more general notion is that of D-cores which +looks at (k, l) restrictions on (in, out) degree. The (k, k) D-core +is the k-core. + +D-cores: Measuring Collaboration of Directed Graphs Based on Degeneracy +Christos Giatsidis, Dimitrios M. Thilikos, Michalis Vazirgiannis, ICDM 2011. +http://www.graphdegeneracy.org/dcores_ICDM_2011.pdf + +Multi-scale structure and topological anomaly detection via a new network \ +statistic: The onion decomposition +L. Hébert-Dufresne, J. A. Grochow, and A. Allard +Scientific Reports 6, 31708 (2016) +http://doi.org/10.1038/srep31708 + +""" +import networkx as nx +from networkx.exception import NetworkXError +from networkx.utils import not_implemented_for + +__all__ = [ + "core_number", + "find_cores", + "k_core", + "k_shell", + "k_crust", + "k_corona", + "k_truss", + "onion_layers", +] + + +@not_implemented_for("multigraph") +def core_number(G): + """Returns the core number for each vertex. + + A k-core is a maximal subgraph that contains nodes of degree k or more. + + The core number of a node is the largest value k of a k-core containing + that node. + + Parameters + ---------- + G : NetworkX graph + A graph or directed graph + + Returns + ------- + core_number : dictionary + A dictionary keyed by node to the core number. + + Raises + ------ + NetworkXError + The k-core is not implemented for graphs with self loops + or parallel edges. + + Notes + ----- + Not implemented for graphs with parallel edges or self loops. + + For directed graphs the node degree is defined to be the + in-degree + out-degree. + + References + ---------- + .. [1] An O(m) Algorithm for Cores Decomposition of Networks + Vladimir Batagelj and Matjaz Zaversnik, 2003. + https://arxiv.org/abs/cs.DS/0310049 + """ + if nx.number_of_selfloops(G) > 0: + msg = ( + "Input graph has self loops which is not permitted; " + "Consider using G.remove_edges_from(nx.selfloop_edges(G))." + ) + raise NetworkXError(msg) + degrees = dict(G.degree()) + # Sort nodes by degree. + nodes = sorted(degrees, key=degrees.get) + bin_boundaries = [0] + curr_degree = 0 + for i, v in enumerate(nodes): + if degrees[v] > curr_degree: + bin_boundaries.extend([i] * (degrees[v] - curr_degree)) + curr_degree = degrees[v] + node_pos = {v: pos for pos, v in enumerate(nodes)} + # The initial guess for the core number of a node is its degree. + core = degrees + nbrs = {v: list(nx.all_neighbors(G, v)) for v in G} + for v in nodes: + for u in nbrs[v]: + if core[u] > core[v]: + nbrs[u].remove(v) + pos = node_pos[u] + bin_start = bin_boundaries[core[u]] + node_pos[u] = bin_start + node_pos[nodes[bin_start]] = pos + nodes[bin_start], nodes[pos] = nodes[pos], nodes[bin_start] + bin_boundaries[core[u]] += 1 + core[u] -= 1 + return core + + +find_cores = core_number + + +def _core_subgraph(G, k_filter, k=None, core=None): + """Returns the subgraph induced by nodes passing filter `k_filter`. + + Parameters + ---------- + G : NetworkX graph + The graph or directed graph to process + k_filter : filter function + This function filters the nodes chosen. It takes three inputs: + A node of G, the filter's cutoff, and the core dict of the graph. + The function should return a Boolean value. + k : int, optional + The order of the core. If not specified use the max core number. + This value is used as the cutoff for the filter. + core : dict, optional + Precomputed core numbers keyed by node for the graph `G`. + If not specified, the core numbers will be computed from `G`. + + """ + if core is None: + core = core_number(G) + if k is None: + k = max(core.values()) + nodes = (v for v in core if k_filter(v, k, core)) + return G.subgraph(nodes).copy() + + +def k_core(G, k=None, core_number=None): + """Returns the k-core of G. + + A k-core is a maximal subgraph that contains nodes of degree k or more. + + Parameters + ---------- + G : NetworkX graph + A graph or directed graph + k : int, optional + The order of the core. If not specified return the main core. + core_number : dictionary, optional + Precomputed core numbers for the graph G. + + Returns + ------- + G : NetworkX graph + The k-core subgraph + + Raises + ------ + NetworkXError + The k-core is not defined for graphs with self loops or parallel edges. + + Notes + ----- + The main core is the core with the largest degree. + + Not implemented for graphs with parallel edges or self loops. + + For directed graphs the node degree is defined to be the + in-degree + out-degree. + + Graph, node, and edge attributes are copied to the subgraph. + + See Also + -------- + core_number + + References + ---------- + .. [1] An O(m) Algorithm for Cores Decomposition of Networks + Vladimir Batagelj and Matjaz Zaversnik, 2003. + https://arxiv.org/abs/cs.DS/0310049 + """ + + def k_filter(v, k, c): + return c[v] >= k + + return _core_subgraph(G, k_filter, k, core_number) + + +def k_shell(G, k=None, core_number=None): + """Returns the k-shell of G. + + The k-shell is the subgraph induced by nodes with core number k. + That is, nodes in the k-core that are not in the (k+1)-core. + + Parameters + ---------- + G : NetworkX graph + A graph or directed graph. + k : int, optional + The order of the shell. If not specified return the outer shell. + core_number : dictionary, optional + Precomputed core numbers for the graph G. + + + Returns + ------- + G : NetworkX graph + The k-shell subgraph + + Raises + ------ + NetworkXError + The k-shell is not implemented for graphs with self loops + or parallel edges. + + Notes + ----- + This is similar to k_corona but in that case only neighbors in the + k-core are considered. + + Not implemented for graphs with parallel edges or self loops. + + For directed graphs the node degree is defined to be the + in-degree + out-degree. + + Graph, node, and edge attributes are copied to the subgraph. + + See Also + -------- + core_number + k_corona + + + References + ---------- + .. [1] A model of Internet topology using k-shell decomposition + Shai Carmi, Shlomo Havlin, Scott Kirkpatrick, Yuval Shavitt, + and Eran Shir, PNAS July 3, 2007 vol. 104 no. 27 11150-11154 + http://www.pnas.org/content/104/27/11150.full + """ + + def k_filter(v, k, c): + return c[v] == k + + return _core_subgraph(G, k_filter, k, core_number) + + +def k_crust(G, k=None, core_number=None): + """Returns the k-crust of G. + + The k-crust is the graph G with the k-core removed. + + Parameters + ---------- + G : NetworkX graph + A graph or directed graph. + k : int, optional + The order of the shell. If not specified return the main crust. + core_number : dictionary, optional + Precomputed core numbers for the graph G. + + Returns + ------- + G : NetworkX graph + The k-crust subgraph + + Raises + ------ + NetworkXError + The k-crust is not implemented for graphs with self loops + or parallel edges. + + Notes + ----- + This definition of k-crust is different than the definition in [1]_. + The k-crust in [1]_ is equivalent to the k+1 crust of this algorithm. + + Not implemented for graphs with parallel edges or self loops. + + For directed graphs the node degree is defined to be the + in-degree + out-degree. + + Graph, node, and edge attributes are copied to the subgraph. + + See Also + -------- + core_number + + References + ---------- + .. [1] A model of Internet topology using k-shell decomposition + Shai Carmi, Shlomo Havlin, Scott Kirkpatrick, Yuval Shavitt, + and Eran Shir, PNAS July 3, 2007 vol. 104 no. 27 11150-11154 + http://www.pnas.org/content/104/27/11150.full + """ + # Default for k is one less than in _core_subgraph, so just inline. + # Filter is c[v] <= k + if core_number is None: + core_number = find_cores(G) + if k is None: + k = max(core_number.values()) - 1 + nodes = (v for v in core_number if core_number[v] <= k) + return G.subgraph(nodes).copy() + + +def k_corona(G, k, core_number=None): + """Returns the k-corona of G. + + The k-corona is the subgraph of nodes in the k-core which have + exactly k neighbours in the k-core. + + Parameters + ---------- + G : NetworkX graph + A graph or directed graph + k : int + The order of the corona. + core_number : dictionary, optional + Precomputed core numbers for the graph G. + + Returns + ------- + G : NetworkX graph + The k-corona subgraph + + Raises + ------ + NetworkXError + The k-cornoa is not defined for graphs with self loops or + parallel edges. + + Notes + ----- + Not implemented for graphs with parallel edges or self loops. + + For directed graphs the node degree is defined to be the + in-degree + out-degree. + + Graph, node, and edge attributes are copied to the subgraph. + + See Also + -------- + core_number + + References + ---------- + .. [1] k -core (bootstrap) percolation on complex networks: + Critical phenomena and nonlocal effects, + A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, + Phys. Rev. E 73, 056101 (2006) + http://link.aps.org/doi/10.1103/PhysRevE.73.056101 + """ + + def func(v, k, c): + return c[v] == k and k == sum(1 for w in G[v] if c[w] >= k) + + return _core_subgraph(G, func, k, core_number) + + +@not_implemented_for("directed") +@not_implemented_for("multigraph") +def k_truss(G, k): + """Returns the k-truss of `G`. + + The k-truss is the maximal induced subgraph of `G` which contains at least + three vertices where every edge is incident to at least `k-2` triangles. + + Parameters + ---------- + G : NetworkX graph + An undirected graph + k : int + The order of the truss + + Returns + ------- + H : NetworkX graph + The k-truss subgraph + + Raises + ------ + NetworkXError + + The k-truss is not defined for graphs with self loops or parallel edges + or directed graphs. + + Notes + ----- + A k-clique is a (k-2)-truss and a k-truss is a (k+1)-core. + + Not implemented for digraphs or graphs with parallel edges or self loops. + + Graph, node, and edge attributes are copied to the subgraph. + + K-trusses were originally defined in [2] which states that the k-truss + is the maximal induced subgraph where each edge belongs to at least + `k-2` triangles. A more recent paper, [1], uses a slightly different + definition requiring that each edge belong to at least `k` triangles. + This implementation uses the original definition of `k-2` triangles. + + References + ---------- + .. [1] Bounds and Algorithms for k-truss. Paul Burkhardt, Vance Faber, + David G. Harris, 2018. https://arxiv.org/abs/1806.05523v2 + .. [2] Trusses: Cohesive Subgraphs for Social Network Analysis. Jonathan + Cohen, 2005. + """ + H = G.copy() + + n_dropped = 1 + while n_dropped > 0: + n_dropped = 0 + to_drop = [] + seen = set() + for u in H: + nbrs_u = set(H[u]) + seen.add(u) + new_nbrs = [v for v in nbrs_u if v not in seen] + for v in new_nbrs: + if len(nbrs_u & set(H[v])) < (k - 2): + to_drop.append((u, v)) + H.remove_edges_from(to_drop) + n_dropped = len(to_drop) + H.remove_nodes_from(list(nx.isolates(H))) + + return H + + +@not_implemented_for("multigraph") +@not_implemented_for("directed") +def onion_layers(G): + """Returns the layer of each vertex in an onion decomposition of the graph. + + The onion decomposition refines the k-core decomposition by providing + information on the internal organization of each k-shell. It is usually + used alongside the `core numbers`. + + Parameters + ---------- + G : NetworkX graph + A simple graph without self loops or parallel edges + + Returns + ------- + od_layers : dictionary + A dictionary keyed by vertex to the onion layer. The layers are + contiguous integers starting at 1. + + Raises + ------ + NetworkXError + The onion decomposition is not implemented for graphs with self loops + or parallel edges or for directed graphs. + + Notes + ----- + Not implemented for graphs with parallel edges or self loops. + + Not implemented for directed graphs. + + See Also + -------- + core_number + + References + ---------- + .. [1] Multi-scale structure and topological anomaly detection via a new + network statistic: The onion decomposition + L. Hébert-Dufresne, J. A. Grochow, and A. Allard + Scientific Reports 6, 31708 (2016) + http://doi.org/10.1038/srep31708 + .. [2] Percolation and the effective structure of complex networks + A. Allard and L. Hébert-Dufresne + Physical Review X 9, 011023 (2019) + http://doi.org/10.1103/PhysRevX.9.011023 + """ + if nx.number_of_selfloops(G) > 0: + msg = ( + "Input graph contains self loops which is not permitted; " + "Consider using G.remove_edges_from(nx.selfloop_edges(G))." + ) + raise NetworkXError(msg) + # Dictionaries to register the k-core/onion decompositions. + od_layers = {} + # Adjacency list + neighbors = {v: list(nx.all_neighbors(G, v)) for v in G} + # Effective degree of nodes. + degrees = dict(G.degree()) + # Performs the onion decomposition. + current_core = 1 + current_layer = 1 + # Sets vertices of degree 0 to layer 1, if any. + isolated_nodes = [v for v in nx.isolates(G)] + if len(isolated_nodes) > 0: + for v in isolated_nodes: + od_layers[v] = current_layer + degrees.pop(v) + current_layer = 2 + # Finds the layer for the remaining nodes. + while len(degrees) > 0: + # Sets the order for looking at nodes. + nodes = sorted(degrees, key=degrees.get) + # Sets properly the current core. + min_degree = degrees[nodes[0]] + if min_degree > current_core: + current_core = min_degree + # Identifies vertices in the current layer. + this_layer = [] + for n in nodes: + if degrees[n] > current_core: + break + this_layer.append(n) + # Identifies the core/layer of the vertices in the current layer. + for v in this_layer: + od_layers[v] = current_layer + for n in neighbors[v]: + neighbors[n].remove(v) + degrees[n] = degrees[n] - 1 + degrees.pop(v) + # Updates the layer count. + current_layer = current_layer + 1 + # Returns the dictionaries containing the onion layer of each vertices. + return od_layers