Note
This documents the development version of NetworkX. Documentation for the current release can be found here.
networkx.algorithms.summarization.dedensify¶

dedensify
(G, threshold, prefix=None, copy=True)[source]¶ Compresses neighborhoods around highdegree nodes
Reduces the number of edges to highdegree nodes by adding compressor nodes that summarize multiple edges of the same type to highdegree nodes (nodes with a degree greater than a given threshold). Dedensification also has the added benefit of reducing the number of edges around highdegree nodes. The implementation currently supports graphs with a single edge type.
 Parameters
 G: graph
A networkx graph
 threshold: int
Minimum degree threshold of a node to be considered a high degree node. The threshold must be greater than or equal to 2.
 prefix: str or None, optional (default: None)
An optional prefix for denoting compressor nodes
 copy: bool, optional (default: True)
Indicates if dedensification should be done inplace
 Returns
 dedensified networkx graph(graph, set)
2tuple of the dedensified graph and set of compressor nodes
Notes
According to the algorithm in [1], removes edges in a graph by compressing/decompressing the neighborhoods around high degree nodes by adding compressor nodes that summarize multiple edges of the same type to highdegree nodes. Dedensification will only add a compressor node when doing so will reduce the total number of edges in the given graph. This implementation currently supports graphs with a single edge type.
References
 1
Maccioni, A., & Abadi, D. J. (2016, August). Scalable pattern matching over compressed graphs via dedensification. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 17551764). http://www.cs.umd.edu/~abadi/papers/graphdedense.pdf
Examples
Dedensification will only add compressor nodes when doing so would result in fewer edges:
>>> original_graph = nx.DiGraph() >>> original_graph.add_nodes_from( ... ["1", "2", "3", "4", "5", "6", "A", "B", "C"] ... ) >>> original_graph.add_edges_from( ... [ ... ("1", "C"), ("1", "B"), ... ("2", "C"), ("2", "B"), ("2", "A"), ... ("3", "B"), ("3", "A"), ("3", "6"), ... ("4", "C"), ("4", "B"), ("4", "A"), ... ("5", "B"), ("5", "A"), ... ("6", "5"), ... ("A", "6") ... ] ... ) >>> c_graph, c_nodes = nx.dedensify(original_graph, threshold=2) >>> original_graph.number_of_edges() 15 >>> c_graph.number_of_edges() 14
A dedensified, directed graph can be “densified” to reconstruct the original graph:
>>> original_graph = nx.DiGraph() >>> original_graph.add_nodes_from( ... ["1", "2", "3", "4", "5", "6", "A", "B", "C"] ... ) >>> original_graph.add_edges_from( ... [ ... ("1", "C"), ("1", "B"), ... ("2", "C"), ("2", "B"), ("2", "A"), ... ("3", "B"), ("3", "A"), ("3", "6"), ... ("4", "C"), ("4", "B"), ("4", "A"), ... ("5", "B"), ("5", "A"), ... ("6", "5"), ... ("A", "6") ... ] ... ) >>> c_graph, c_nodes = nx.dedensify(original_graph, threshold=2) >>> # redensifies the compressed graph into the original graph >>> for c_node in c_nodes: ... all_neighbors = set(nx.all_neighbors(c_graph, c_node)) ... out_neighbors = set(c_graph.neighbors(c_node)) ... for out_neighbor in out_neighbors: ... c_graph.remove_edge(c_node, out_neighbor) ... in_neighbors = all_neighbors  out_neighbors ... for in_neighbor in in_neighbors: ... c_graph.remove_edge(in_neighbor, c_node) ... for out_neighbor in out_neighbors: ... c_graph.add_edge(in_neighbor, out_neighbor) ... c_graph.remove_node(c_node) ... >>> nx.is_isomorphic(original_graph, c_graph) True