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Graph Measures

Graph measures or metrics are values that capture graph properties like efficiency. As these measures capture information across the entire graph, or for nodes, edges or subgraphs, they can be used to study graph properties. These measures can also be used as a low-dimensional representation of the graph in machine learning tasks. Since graph measures capture information across the entire graph, they make use of information that would otherwise be lost if one chose to only use node features or a vectorized connectivity matrix for example.


The GraphMeasureTransform class is a class for extracting graph measures from graphs. A range of networkx graph measures is available and can be used in a PHOTON pipeline or extracted and written to a csv file for further use.


Name Type Description Default
graph_functions dict

a dict of graph functions to calculate with keys as the networkx function name and a dict of the arguments as the value. In this second dictionary, the keys are the functions arguments and values are the desired values for the argument.

adjacency_axis int

Channel index for adjacency

logs str

path to the log data

n_processes int

Number of processes for multi processing



measuretrans = GraphMeasureTransform(graph_functions={"large_clique_size": {},
                                                      "global_efficiency": {},
                                                      "overall_reciprocity": {},
                                                      "local_efficiency": {}})

Available Measures

The following measures are available. They are different networkx functions that calculate these measures. Be warned that, depending on your graph, these measures might take very long to calculate. Also some measures are only available as part of a pipeline, while some are also available for extraction (see accompanying table).

Measure Name in Dict available for extract
Node connectivity for all pairs all_pairs_node_connectivity Yes
Local node connectivity local_node_connectivity Yes
Node connectivity node_connectivity Yes
K component structure k_components No
large clique size large_clique_size Yes
Average clustering Coefficient average_clustering Yes
Treewidth decomposition (Minimum Degree Heuristic) treewidth_min_degree No
Treewidth decomposition (Minimum Fill-in heuristic) treewidth_min_fill_in No
Degree assortativity of graph degree_assortativity_coefficient Yes
Attribute assortativity of graph attribute_assortativity_coefficient Yes
Numeric assortativity of graph numeric_assortativity_coefficient Yes
Degree assortaivity of graph (scipy implmenetation) degree_pearson_correlation_coefficient Yes
Average neighbour degree node-wise average_neighbor_degree Yes
Average degree connectivity of graph average_degree_connectivity No
Average degree connectivity of graph (kNN implementation) k_nearest_neighbors No
Degree centrality (node-wise) degree_centrality Yes
In-degree centrality (node-wise) in_degree_centrality Yes
Out-degree centrality (node-wise) out_degree_centrality Yes
Eigenvector centrality (node-wise) eigenvector_centrality Yes
Katz centrality (node-wise) katz_centrality Yes
Closeness centrality (node-wise) closeness_centrality Yes
Incremental closeness centrality (node-wise) incremental_closeness_centrality Yes
Current flow closeness centrality (node-wise) current_flow_closeness_centrality Yes
Information centrality (node-wise) information_centrality Yes
Betweeness centrality (node-wise) betweenness_centrality Yes
Betweeness centrality (node-wise) on a subset of nodes betweenness_centrality_subset No
Betweeness centrality (edge-wise) on a subset of edges edge_betweenness_centrality_subset No
Current flow betweeness centrality (node-wise) current_flow_betweenness_centrality Yes
Current flow betweeness centrality (edge-wise) enedge_current_flow_betweenness_centrality Yes
Approximate current flow betweeness centrality (node-wise) approximate_current_flow_betweenness_centrality Yes
Current flow betweeness centrality (node-wise) on a subset of nodes current_flow_betweenness_centrality_subset Yes
Current flow betweeness centrality (edge-wise) on a subset of edges edge_current_flow_betweenness_centrality_subset Yes
Communicability betweeness centrality (noe-wise) communicability_betweenness_centrality Yes
Betweeness centrality (group-wise) group_betweenness_centrality Yes
Closeness centrality (group-wise) group_closeness_centrality Yes
Degree centrality (group-wise) group_degree_centrality Yes
In-degree centrality (group-wise) group_in_degree_centrality Yes
Out-degree centrality (group-wise) group_out_degree_centrality Yes
Load centrality (node-wise) load_centrality Yes
Load centrality (edge-wise) edge_load_centrality Yes
Subgraph centrality (node-wise) subgraph_centrality Yes
Subgraph centrality (node-wise, exponent implementation) subgraph_centrality_exp Yes
Estrada Index estrada_index Yes
Harmonic centrality (node-wise) harmonic_centrality Yes
Dispersion dispersion No
Local reaching centrality local_reaching_centrality Yes
Global reaching centrality global_reaching_centrality Yes
Perlocation centrality (node-wise) percolation_centrality Yes
Second-order centrality (node-wise) second_order_centrality Yes
Voterank via VoteRank algorithm voterank No
Size of largest clique graph_clique_number Yes
Number of maximal cliques in graph graph_number_of_cliques Yes
Size of largest clique containing each specified node node_clique_number Yes
Number of cliques for each specified node number_of_cliques Yes
Number of Triangles triangles Yes
Transivity transitivity Yes
Clustering coefficient for specified nodes clustering No
Square Clustering (node-wise) square_clustering Yes
Communicability communicability No
Communicability (exponent implmenetation) communicability_exp No
Number of connected components number_connected_components Yes
Number of strongly connected components number_strongly_connected_components Yes
Number of weakly connected components number_weakly_connected_components Yes
Number of attracting components number_attracting_components Yes
Average Node connectivity average_node_connectivity Yes
Edge connectivity edge_connectivity Yes
Local Edge connectivity local_edge_connectivity Yes
Core number (node-wise) core_number Yes
Onion layers (node-wise) onion_layers Yes
Boundary expansion (set-wise) boundary_expansion Yes
Conductance between two sets of nodes conductance Yes
Cut size between two sets of nodes cut_size Yes
Edge expansion between two sets of nodes edge_expansion Yes
Mixing expansion between two sets of nodes mixing_expansion Yes
Volume between two sets of nodes volume Yes
Diameter diameter Yes
Eccentricity eccentricity Yes
Radius radius Yes
Resistance Distance between node A and B resistance_distance Yes
Efficiency between node A and B efficiency Yes
Local efficiency local_efficiency Yes
Global efficiency global_efficiency Yes
Flow hierarchy flow_hierarchy Yes
Number of isolates number_of_isolates Yes
PageRank value (node-wise) pagerank Yes
HITS hubs and authorities hits No
Non-randomness non_randomness No
Reciprocity (node-wise) reciprocity Yes
Overall reciprocity overall_reciprocity Yes
Rich-club coefficient rich_club_coefficient Yes
Average shortest path length average_shortest_path_length Yes
Small-world coefficient sigma sigma Yes
Small-world coefficient omega omega Yes
S-metric s_metric Yes
Constraint (node-wise) constraint Yes
Effective Size (node-wise) effective_size Yes
Local constraint of node A with respect to node B local_constraint Yes
Triadic census triadic_census No
Closeness vitality closeness_vitality No
Wiener Index wiener_index Yes