## Mercurial > repos > shellac > sam_consensus_v3

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

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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

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

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"""Hubs and authorities analysis of graph structure. """ import networkx as nx __all__ = ["hits", "hits_numpy", "hits_scipy", "authority_matrix", "hub_matrix"] def hits(G, max_iter=100, tol=1.0e-8, nstart=None, normalized=True): """Returns HITS hubs and authorities values for nodes. The HITS algorithm computes two numbers for a node. Authorities estimates the node value based on the incoming links. Hubs estimates the node value based on outgoing links. Parameters ---------- G : graph A NetworkX graph max_iter : integer, optional Maximum number of iterations in power method. tol : float, optional Error tolerance used to check convergence in power method iteration. nstart : dictionary, optional Starting value of each node for power method iteration. normalized : bool (default=True) Normalize results by the sum of all of the values. Returns ------- (hubs,authorities) : two-tuple of dictionaries Two dictionaries keyed by node containing the hub and authority values. Raises ------ PowerIterationFailedConvergence If the algorithm fails to converge to the specified tolerance within the specified number of iterations of the power iteration method. Examples -------- >>> G = nx.path_graph(4) >>> h, a = nx.hits(G) Notes ----- The eigenvector calculation is done by the power iteration method and has no guarantee of convergence. The iteration will stop after max_iter iterations or an error tolerance of number_of_nodes(G)*tol has been reached. The HITS algorithm was designed for directed graphs but this algorithm does not check if the input graph is directed and will execute on undirected graphs. References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Jon Kleinberg, Authoritative sources in a hyperlinked environment Journal of the ACM 46 (5): 604-32, 1999. doi:10.1145/324133.324140. http://www.cs.cornell.edu/home/kleinber/auth.pdf. """ if type(G) == nx.MultiGraph or type(G) == nx.MultiDiGraph: raise Exception("hits() not defined for graphs with multiedges.") if len(G) == 0: return {}, {} # choose fixed starting vector if not given if nstart is None: h = dict.fromkeys(G, 1.0 / G.number_of_nodes()) else: h = nstart # normalize starting vector s = 1.0 / sum(h.values()) for k in h: h[k] *= s for _ in range(max_iter): # power iteration: make up to max_iter iterations hlast = h h = dict.fromkeys(hlast.keys(), 0) a = dict.fromkeys(hlast.keys(), 0) # this "matrix multiply" looks odd because it is # doing a left multiply a^T=hlast^T*G for n in h: for nbr in G[n]: a[nbr] += hlast[n] * G[n][nbr].get("weight", 1) # now multiply h=Ga for n in h: for nbr in G[n]: h[n] += a[nbr] * G[n][nbr].get("weight", 1) # normalize vector s = 1.0 / max(h.values()) for n in h: h[n] *= s # normalize vector s = 1.0 / max(a.values()) for n in a: a[n] *= s # check convergence, l1 norm err = sum([abs(h[n] - hlast[n]) for n in h]) if err < tol: break else: raise nx.PowerIterationFailedConvergence(max_iter) if normalized: s = 1.0 / sum(a.values()) for n in a: a[n] *= s s = 1.0 / sum(h.values()) for n in h: h[n] *= s return h, a def authority_matrix(G, nodelist=None): """Returns the HITS authority matrix.""" M = nx.to_numpy_array(G, nodelist=nodelist) return M.T @ M def hub_matrix(G, nodelist=None): """Returns the HITS hub matrix.""" M = nx.to_numpy_array(G, nodelist=nodelist) return M @ M.T def hits_numpy(G, normalized=True): """Returns HITS hubs and authorities values for nodes. The HITS algorithm computes two numbers for a node. Authorities estimates the node value based on the incoming links. Hubs estimates the node value based on outgoing links. Parameters ---------- G : graph A NetworkX graph normalized : bool (default=True) Normalize results by the sum of all of the values. Returns ------- (hubs,authorities) : two-tuple of dictionaries Two dictionaries keyed by node containing the hub and authority values. Examples -------- >>> G = nx.path_graph(4) >>> h, a = nx.hits(G) Notes ----- The eigenvector calculation uses NumPy's interface to LAPACK. The HITS algorithm was designed for directed graphs but this algorithm does not check if the input graph is directed and will execute on undirected graphs. References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Jon Kleinberg, Authoritative sources in a hyperlinked environment Journal of the ACM 46 (5): 604-32, 1999. doi:10.1145/324133.324140. http://www.cs.cornell.edu/home/kleinber/auth.pdf. """ try: import numpy as np except ImportError as e: raise ImportError("hits_numpy() requires NumPy: " "http://numpy.org/") from e if len(G) == 0: return {}, {} H = nx.hub_matrix(G, list(G)) e, ev = np.linalg.eig(H) m = e.argsort()[-1] # index of maximum eigenvalue h = np.array(ev[:, m]).flatten() A = nx.authority_matrix(G, list(G)) e, ev = np.linalg.eig(A) m = e.argsort()[-1] # index of maximum eigenvalue a = np.array(ev[:, m]).flatten() if normalized: h = h / h.sum() a = a / a.sum() else: h = h / h.max() a = a / a.max() hubs = dict(zip(G, map(float, h))) authorities = dict(zip(G, map(float, a))) return hubs, authorities def hits_scipy(G, max_iter=100, tol=1.0e-6, normalized=True): """Returns HITS hubs and authorities values for nodes. The HITS algorithm computes two numbers for a node. Authorities estimates the node value based on the incoming links. Hubs estimates the node value based on outgoing links. Parameters ---------- G : graph A NetworkX graph max_iter : integer, optional Maximum number of iterations in power method. tol : float, optional Error tolerance used to check convergence in power method iteration. nstart : dictionary, optional Starting value of each node for power method iteration. normalized : bool (default=True) Normalize results by the sum of all of the values. Returns ------- (hubs,authorities) : two-tuple of dictionaries Two dictionaries keyed by node containing the hub and authority values. Examples -------- >>> G = nx.path_graph(4) >>> h, a = nx.hits(G) Notes ----- This implementation uses SciPy sparse matrices. The eigenvector calculation is done by the power iteration method and has no guarantee of convergence. The iteration will stop after max_iter iterations or an error tolerance of number_of_nodes(G)*tol has been reached. The HITS algorithm was designed for directed graphs but this algorithm does not check if the input graph is directed and will execute on undirected graphs. Raises ------ PowerIterationFailedConvergence If the algorithm fails to converge to the specified tolerance within the specified number of iterations of the power iteration method. References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Jon Kleinberg, Authoritative sources in a hyperlinked environment Journal of the ACM 46 (5): 604-632, 1999. doi:10.1145/324133.324140. http://www.cs.cornell.edu/home/kleinber/auth.pdf. """ try: import numpy as np except ImportError as e: raise ImportError( "hits_scipy() requires SciPy and NumPy:" "http://scipy.org/ http://numpy.org/" ) from e if len(G) == 0: return {}, {} M = nx.to_scipy_sparse_matrix(G, nodelist=list(G)) (n, m) = M.shape # should be square A = M.T * M # authority matrix x = np.ones((n, 1)) / n # initial guess # power iteration on authority matrix i = 0 while True: xlast = x x = A * x x = x / x.max() # check convergence, l1 norm err = np.absolute(x - xlast).sum() if err < tol: break if i > max_iter: raise nx.PowerIterationFailedConvergence(max_iter) i += 1 a = np.asarray(x).flatten() # h=M*a h = np.asarray(M * a).flatten() if normalized: h = h / h.sum() a = a / a.sum() hubs = dict(zip(G, map(float, h))) authorities = dict(zip(G, map(float, a))) return hubs, authorities