def jaccard_coefficient(G, ebunch=None): """ For NetworkX Compatability. See `jaccard` Parameters ---------- graph : cugraph.Graph cuGraph graph descriptor, should contain the connectivity information as an edge list (edge weights are not used for this algorithm). The graph should be undirected where an undirected edge is represented by a directed edge in both direction. The adjacency list will be computed if not already present. ebunch : cudf.DataFrame A GPU dataframe consisting of two columns representing pairs of vertices. If provided, the jaccard coefficient is computed for the given vertex pairs. If the vertex_pair is not provided then the current implementation computes the jaccard coefficient for all adjacent vertices in the graph. Returns ------- df : cudf.DataFrame GPU data frame of size E (the default) or the size of the given pairs (first, second) containing the Jaccard weights. The ordering is relative to the adjacency list, or that given by the specified vertex pairs. df['source'] : cudf.Series The source vertex ID (will be identical to first if specified) df['destination'] : cudf.Series The destination vertex ID (will be identical to second if specified) df['jaccard_coeff'] : cudf.Series The computed Jaccard coefficient between the source and destination vertices Examples -------- >>> gdf = cudf.read_csv('datasets/karate.csv', delimiter=' ', >>> dtype=['int32', 'int32', 'float32'], header=None) >>> G = cugraph.Graph() >>> G.from_cudf_edgelist(gdf, source='0', destination='1') >>> df = cugraph.jaccard_coefficient(G) """ vertex_pair = None G, isNx = check_nx_graph(G) if isNx is True and ebunch is not None: vertex_pair = cudf.from_pandas(pd.DataFrame(ebunch)) df = jaccard(G, vertex_pair) if isNx is True: df = df_edge_score_to_dictionary(df, k="jaccard_coeff", src="source", dst="destination") return df
def sorensen_coefficient(G, ebunch=None): """ Parameters ---------- G : cugraph.Graph cuGraph Graph instance, should contain the connectivity information as an edge list (edge weights are not used for this algorithm). The graph should be undirected where an undirected edge is represented by a directed edge in both direction. The adjacency list will be computed if not already present. ebunch : cudf.DataFrame, optional (default=None) A GPU dataframe consisting of two columns representing pairs of vertices. If provided, the sorensen coefficient is computed for the given vertex pairs. If the vertex_pair is not provided then the current implementation computes the sorensen coefficient for all adjacent vertices in the graph. Returns ------- df : cudf.DataFrame GPU data frame of size E (the default) or the size of the given pairs (first, second) containing the Sorensen weights. The ordering is relative to the adjacency list, or that given by the specified vertex pairs. df['source'] : cudf.Series The source vertex ID (will be identical to first if specified) df['destination'] : cudf.Series The destination vertex ID (will be identical to second if specified) df['sorensen_coeff'] : cudf.Series The computed sorensen coefficient between the source and destination vertices Examples -------- >>> gdf = cudf.read_csv(datasets_path / 'karate.csv', delimiter=' ', ... dtype=['int32', 'int32', 'float32'], header=None) >>> G = cugraph.Graph() >>> G.from_cudf_edgelist(gdf, source='0', destination='1') >>> df = cugraph.sorensen_coefficient(G) """ vertex_pair = None G, isNx = ensure_cugraph_obj_for_nx(G) if isNx is True and ebunch is not None: vertex_pair = cudf.DataFrame(ebunch) df = sorensen(G, vertex_pair) if isNx is True: df = df_edge_score_to_dictionary(df, k="sorensen_coeff", src="source", dst="destination") return df
def overlap_coefficient(G, ebunch=None): """ NetworkX similar API. See 'jaccard' for a description """ vertex_pair = None G, isNx = check_nx_graph(G) if isNx is True and ebunch is not None: vertex_pair = cudf.from_pandas(pd.DataFrame(ebunch)) df = overlap(G, vertex_pair) if isNx is True: df = df_edge_score_to_dictionary(df, k="overlap_coeff", src="source", dst="destination") return df
def edge_betweenness_centrality(G, k=None, normalized=True, weight=None, seed=None, result_dtype=np.float64): """ Compute the edge betweenness centrality for all edges of the graph G. Betweenness centrality is a measure of the number of shortest paths that pass over an edge. An edge with a high betweenness centrality score has more paths passing over it and is therefore believed to be more important. Rather than doing an all-pair shortest path, a sample of k starting vertices can be used. CuGraph does not currently support the 'weight' parameter as seen in the corresponding networkX call. Parameters ---------- G : cuGraph.Graph or networkx.Graph The graph can be either directed (DiGraph) or undirected (Graph). Weights in the graph are ignored, the current implementation uses BFS traversals. Use weight parameter if weights need to be considered (currently not supported) k : int or list or None, optional, default=None If k is not None, use k node samples to estimate betweenness. Higher values give better approximation If k is a list, use the content of the list for estimation: the list should contain vertices identifiers. Vertices obtained through sampling or defined as a list will be used as sources for traversals inside the algorithm. normalized : bool, optional Default is True. If true, the betweenness values are normalized by 2 / (n * (n - 1)) for Graphs (undirected), and 1 / (n * (n - 1)) for DiGraphs (directed graphs) where n is the number of nodes in G. Normalization will ensure that values are in [0, 1], this normalization scales for the highest possible value where one edge is crossed by every single shortest path. weight : cudf.DataFrame, optional, default=None Specifies the weights to be used for each edge. Should contain a mapping between edges and weights. (Not Supported) seed : optional if k is specified and k is an integer, use seed to initialize the random number generator. Using None as seed relies on random.seed() behavior: using current system time If k is either None or list: seed parameter is ignored result_dtype : np.float32 or np.float64, optional, default=np.float64 Indicate the data type of the betweenness centrality scores Using double automatically switch implementation to "default" Returns ------- df : cudf.DataFrame or Dictionary if using NetworkX GPU data frame containing three cudf.Series of size E: the vertex identifiers of the sources, the vertex identifies of the destinations and the corresponding betweenness centrality values. Please note that the resulting the 'src', 'dst' column might not be in ascending order. df['src'] : cudf.Series Contains the vertex identifiers of the source of each edge df['dst'] : cudf.Series Contains the vertex identifiers of the destination of each edge df['edge_betweenness_centrality'] : cudf.Series Contains the betweenness centrality of edges When using undirected graphs, 'src' and 'dst' only contains elements such that 'src' < 'dst', which might differ from networkx and user's input. Namely edge (1 -> 0) is transformed into (0 -> 1) but contains the betweenness centrality of edge (1 -> 0). Examples -------- >>> gdf = cudf.read_csv('datasets/karate.csv', delimiter=' ', >>> dtype=['int32', 'int32', 'float32'], header=None) >>> G = cugraph.Graph() >>> G.from_cudf_edgelist(gdf, source='0', destination='1') >>> ebc = cugraph.edge_betweenness_centrality(G) """ if weight is not None: raise NotImplementedError("weighted implementation of betweenness " "centrality not currently supported") if result_dtype not in [np.float32, np.float64]: raise TypeError("result type can only be np.float32 or np.float64") G, isNx = cugraph.utilities.check_nx_graph(G) vertices = _initialize_vertices(G, k, seed) df = edge_betweenness_centrality_wrapper.edge_betweenness_centrality( G, normalized, weight, vertices, result_dtype) if G.renumbered: df = G.unrenumber(df, "src") df = G.unrenumber(df, "dst") if type(G) is cugraph.Graph: lower_triangle = df['src'] >= df['dst'] df[["src", "dst"]][lower_triangle] = df[["dst", "src"]][lower_triangle] df = df.groupby(by=["src", "dst"]).sum().reset_index() if isNx is True: return df_edge_score_to_dictionary(df, 'betweenness_centrality') else: return df