easygraph.functions.hypergraph.centrality package
Submodules
easygraph.functions.hypergraph.centrality.cycle_ratio module
- easygraph.functions.hypergraph.centrality.cycle_ratio.StatisticsAndCalculateIndicators(SmallestCyclesOfNodes, CycLenDict)[source]
- easygraph.functions.hypergraph.centrality.cycle_ratio.cycle_ratio_centrality(G)[source]
- Parameters
G (eg.Graph) –
- Returns
cycle ratio centrality of each node in G
- Return type
dict
Example
>>> G = eg.Graph() >>> G.add_edges([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (1, 5), (2, 5)]) >>> cycle_ratio_centrality(G) {1: 4.083333333333333, 2: 4.083333333333333, 3: 2.6666666666666665, 4: 2.6666666666666665, 5: 1.5}
easygraph.functions.hypergraph.centrality.degree module
easygraph.functions.hypergraph.centrality.hypercoreness module
- easygraph.functions.hypergraph.centrality.hypercoreness.frequency_based_hypercoreness(h)[source]
The frequency-based hypercoreness of nodes in hypergraph.
h : easygraph.Hypergraph
- Returns
dict
- Return type
Centrality, where keys are node IDs and values are lists of centralities.
References
Mancastroppa, M., Iacopini, I., Petri, G. et al. Hyper-cores promote localization and efficient seeding in higher-order processes. Nat Commun 14, 6223 (2023). https://doi.org/10.1038/s41467-023-41887-2
- easygraph.functions.hypergraph.centrality.hypercoreness.size_independent_hypercoreness(h)[source]
The size_independent_hypercoreness of nodes in hypergraph.
- Parameters
h (eg.Hypergraph.) –
- Returns
Centrality, where keys are node IDs and values are lists of centralities.
- Return type
dict
References
Mancastroppa, M., Iacopini, I., Petri, G. et al. Hyper-cores promote localization and efficient seeding in higher-order processes. Nat Commun 14, 6223 (2023). https://doi.org/10.1038/s41467-023-41887-2.
easygraph.functions.hypergraph.centrality.s_centrality module
- easygraph.functions.hypergraph.centrality.s_centrality.s_betweenness(H, s=1, n_workers=None)[source]
Computes the betweenness centrality for each edge in the hypergraph.
Computes the betweenness centrality for each edge in the hypergraph.
- Parameters
H (eg.Hypergraph.) – The hypergraph to compute
s (int, optional.) –
- Returns
dict
The keys are the edges and the values are the betweenness centrality.
The betweenness centrality for each edge in the hypergraph.
- easygraph.functions.hypergraph.centrality.s_centrality.s_closeness(H, s=1, n_workers=None)[source]
Compute the closeness centrality for each edge in the hypergraph.
- Parameters
H (eg.Hypergraph.) –
s (int, optional) –
- Return type
dict. The closeness centrality for each edge in the hypergraph. The keys are the edges and the values are the closeness centrality.
- easygraph.functions.hypergraph.centrality.s_centrality.s_eccentricity(H, s=1, edges=True, source=None)[source]
The length of the longest shortest path from a vertex $u$ to every other vertex in the s-linegraph. $V$ = set of vertices in the s-linegraph $d$ = shortest path distance
\[\text{s-ecc}(u) = \text{max}\{d(u,v): v \in V\}\]- Parameters
H (eg.Hypergraph) –
s (int, optional) –
edges (bool, optional) – Indicates if method should compute edge linegraph (default) or node linegraph.
source (str, optional) – Identifier of node or edge of interest for computing centrality
- Returns
returns the s-eccentricity value of the edges(nodes). If source=None a dictionary of values for each s-edge in H is returned. If source then a single value is returned. If the s-linegraph is disconnected, np.inf is returned.
- Return type
dict or float
easygraph.functions.hypergraph.centrality.vector_centrality module
- easygraph.functions.hypergraph.centrality.vector_centrality.vector_centrality(H)[source]
The vector centrality of nodes in the line graph of the hypergraph.
- Parameters
H (eg.Hypergraph) –
- Returns
Centrality, where keys are node IDs and values are lists of centralities.
- Return type
dict
References
“Vector centrality in hypergraphs”, K. Kovalenko, M. Romance, E. Vasilyeva, D. Aleja, R. Criado, D. Musatov, A.M. Raigorodskii, J. Flores, I. Samoylenko, K. Alfaro-Bittner, M. Perc, S. Boccaletti, https://doi.org/10.1016/j.chaos.2022.112397