@@ -20,27 +20,35 @@ graph using k-core decomposition.
2020
2121.. rubric :: Availability
2222
23- .. rubric :: Version 4.1.0
23+ * Version 4.1.0
2424
25- * New experimental function.
25+ * New experimental function.
2626
2727Description
2828-------------------------------------------------------------------------------
2929
3030The **core number ** of a vertex is the largest value :math: `k` such that the
3131vertex belongs to the :math: `k`-core of the graph.
3232
33- **The main characteristics are: **
33+ The :math: `k`-core of a graph is the maximal subgraph in which every vertex has
34+ degree at least :math: `k`. K-core decomposition assigns one core number to each
35+ vertex and is widely used in network analysis to identify densely connected
36+ regions and hierarchical structure.
3437
35- - Works for **undirected ** graphs.
36- - Each vertex has **exactly one ** core number.
37- - **All vertices ** in the graph are returned.
38- - The number of result rows is :math: `|V|`.
39- - Two or more vertices can share the same core number.
40- - The result is ordered by ``node `` ascending.
38+ This implementation works for **undirected ** graphs. Each vertex has exactly one
39+ core number, all vertices in the graph are returned, and the number of result
40+ rows is :math: `|V|`. Two or more vertices can share the same core number. The
41+ result is ordered by ``node `` ascending.
4142
4243- Running time: :math: `O(m)`
4344
45+ |Boost | Boost Graph Inside
46+
47+ .. rubric :: References
48+
49+ * Batagelj, V. and Zaversnik, M. (2003). An O(m) Algorithm for Cores Decomposition
50+ of Networks. arXiv:cs/0310049.
51+
4452Signatures
4553-------------------------------------------------------------------------------
4654
@@ -80,27 +88,28 @@ Result columns
8088-------------------------------------------------------------------------------
8189
8290.. list-table ::
83- :width: 81
84- :widths: auto
85- :header-rows: 1
86-
87- * - Column
88- - Type
89- - Description
90- * - ``seq ``
91- - ``BIGINT ``
92- - Sequential value starting from 1.
93- * - ``node ``
94- - ``BIGINT ``
95- - Identifier of the vertex.
96- * - ``core ``
97- - ``BIGINT ``
98- - Core number of the vertex.
91+ :width: 81
92+ :widths: auto
93+ :header-rows: 1
94+
95+ * - Column
96+ - Type
97+ - Description
98+ * - ``seq ``
99+ - ``BIGINT ``
100+ - Sequential value starting from 1.
101+ * - ``node ``
102+ - ``BIGINT ``
103+ - Identifier of the vertex.
104+ * - ``core ``
105+ - ``BIGINT ``
106+ - Core number of the vertex.
99107
100108See Also
101109-------------------------------------------------------------------------------
102110
103111* :doc: `sampledata `
112+ * :doc: `pgr_betweennessCentrality `
104113* :doc: `metrics-family `
105114
106115.. rubric :: Indices and tables
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