Add tensor centralities (#600)

* Added tensor methods * added tensor centralities * update * add refs * add ref * added unit tests * Update xgi/algorithms/centrality.py Co-authored-by: Maxime Lucas <[email protected]> * Update xgi/algorithms/centrality.py Co-authored-by: Maxime Lucas <[email protected]> * rename measures * add centralities to nodestats * add docs for tensor methods * add notebook * Update comparing_centralities.ipynb * fix node_edge_centrality * update notebook * add notebook to docs * removed assets * change order of case studies and cookbook * added to "see also" * add docstrings and cleanup function * Update tensor.py * rename things * added test to catch the array helper function * added docstrings * add test that the node-edge centrality converges * add test * Update test_centrality.py --------- Co-authored-by: Maxime Lucas <[email protected]>
xgi-org · Nov 12, 2024 · 1bdba44 · 1bdba44
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diff --git a/LICENSE.md b/LICENSE.md
@@ -31,3 +31,24 @@ DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+---------------------------------
+
+License
+
+Tensor methods for nonuniform hypergraphs
+
+* Tensor methods functionality for the CompleX Group Interactions library
+
+Copyright 2023, 2024 Battelle Memorial Institute
+
+Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+
+1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
+
+3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/docs/source/api/algorithms/xgi.algorithms.centrality.rst b/docs/source/api/algorithms/xgi.algorithms.centrality.rst
@@ -9,6 +9,8 @@ xgi.algorithms.centrality
 
    .. autofunction:: clique_eigenvector_centrality
    .. autofunction:: h_eigenvector_centrality
+   .. autofunction:: z_eigenvector_centrality
    .. autofunction:: node_edge_centrality
    .. autofunction:: line_vector_centrality
    .. autofunction:: katz_centrality
+   .. autofunction:: uniform_h_eigenvector_centrality
diff --git a/docs/source/api/stats/xgi.stats.nodestats.rst b/docs/source/api/stats/xgi.stats.nodestats.rst
@@ -9,12 +9,14 @@
 
    .. autofunction:: attrs
    .. autofunction:: average_neighbor_degree
-   .. autofunction:: clique_eigenvector_centrality
-   .. autofunction:: clustering_coefficient
    .. autofunction:: degree
+   .. autofunction:: clique_eigenvector_centrality
    .. autofunction:: h_eigenvector_centrality
-   .. autofunction:: local_clustering_coefficient
+   .. autofunction:: z_eigenvector_centrality
+   .. autofunction:: katz_centrality
    .. autofunction:: node_edge_centrality
+   .. autofunction:: clustering_coefficient
+   .. autofunction:: local_clustering_coefficient
    .. autofunction:: two_node_clustering_coefficient
    .. autofunction:: local_simplicial_fraction
    .. autofunction:: local_edit_simpliciality

diff --git a/docs/source/api/tutorials/case_studies.rst b/docs/source/api/tutorials/case_studies.rst
@@ -8,4 +8,5 @@ Case studies
    :maxdepth: 1
 
    case_study_1
-   case_study_2
+   case_study_2
+   case_study_3
diff --git a/docs/source/api/tutorials/case_study_3.nblink b/docs/source/api/tutorials/case_study_3.nblink
@@ -0,0 +1,3 @@
+{
+    "path": "../../../../tutorials/case_studies/comparing_centralities.ipynb"
+}
diff --git a/docs/source/user_guides.rst b/docs/source/user_guides.rst
@@ -59,39 +59,38 @@ User Guides
             To the in-depth tutorials
 
 .. grid::
-
+	
     .. grid-item-card:: 
     	:text-align: center
 
-    	Cookbook
+    	Case studies
     	^^^
 
-    	Recipes to solve specific tasks in a few lines
-
+    	To see how others have used XGI in their work
     	+++
 
-        .. button-ref:: api/tutorials/recipes
+        .. button-ref:: api/tutorials/case_studies
             :expand:
             :color: secondary
             :click-parent:
 
-            To the cookbook
-	
+            To the case studies
+    
     .. grid-item-card:: 
     	:text-align: center
 
-    	Case studies
+    	Cookbook
     	^^^
 
-    	To see how others have used XGI in their work
+    	Recipes to solve specific tasks in a few lines
+
     	+++
 
-        .. button-ref:: api/tutorials/case_studies
+        .. button-ref:: api/tutorials/recipes
             :expand:
             :color: secondary
             :click-parent:
 
-            To the case studies
-
+            To the cookbook
 
 For all specifications and options of a particular function, or to explore all existing functions, see the `API Reference <reference.html>`_.
diff --git a/docs/source/using-xgi.rst b/docs/source/using-xgi.rst
@@ -12,6 +12,11 @@ Published work
 2024
 ----
 
+Sinan G. Aksoy, Ilya Amburg, and Stephen J. Young, "Scalable Tensor Methods for Nonuniform Hypergraphs", *SIAM Journal on Mathematics of Data Science*, Vol. 6, Iss. 2, 481-503 (2024).
+
+:bdg-link-primary-line:`Paper <https://doi.org/10.1137/23M1584472>`
+:bdg-link-primary-line:`Code <https://github.com/pnnl/GENTTSV>`
+
 Gonzalo Contreras-Aso, Regino Criado, and Miguel Romance, "Beyond directed hypergraphs: heterogeneous hypergraphs and spectral centralities", *Journal of Complex Networks*, Volume 12, Issue 4, cnae037 (2024).
 
 :bdg-link-primary-line:`Paper <https://doi.org/10.1093/comnet/cnae037>`

diff --git a/tests/algorithms/test_centrality.py b/tests/algorithms/test_centrality.py
@@ -28,47 +28,54 @@ def test_clique_eigenvector_centrality():
     H = xgi.sunflower(3, 1, 3)
     c = H.nodes.clique_eigenvector_centrality.asnumpy()
     assert norm(c[1:] - c[1]) < 1e-4
-    assert abs(c[0] / c[1] - ratio(3, 3, kind="CEC")) < 1e-4
+    assert abs(c[0] / c[1] - _ratio(3, 3, kind="CEC")) < 1e-4
 
     H = xgi.sunflower(5, 1, 7)
     c = H.nodes.clique_eigenvector_centrality.asnumpy()
     assert norm(c[1:] - c[1]) < 1e-4
-    assert abs(c[0] / c[1] - ratio(5, 7, kind="CEC")) < 1e-4
+    assert abs(c[0] / c[1] - _ratio(5, 7, kind="CEC")) < 1e-4
 
 
 @pytest.mark.slow
-def test_h_eigenvector_centrality():
+def test_uniform_h_eigenvector_centrality():
     # test empty hypergraph
     H = xgi.Hypergraph()
-    c = xgi.h_eigenvector_centrality(H)
+    c = xgi.uniform_h_eigenvector_centrality(H)
     assert c == dict()
 
     # Test no edges
     H.add_nodes_from([0, 1, 2])
-    hec = xgi.h_eigenvector_centrality(H)
+    hec = xgi.uniform_h_eigenvector_centrality(H)
     for i in hec:
         assert np.isnan(hec[i])
 
     # test disconnected
     H.add_edge([0, 1])
-    hec = xgi.h_eigenvector_centrality(H)
+    hec = xgi.uniform_h_eigenvector_centrality(H)
     assert set(hec) == {0, 1, 2}
     for i in hec:
         assert np.isnan(hec[i])
 
     H = xgi.sunflower(3, 1, 5)
-    c = H.nodes.h_eigenvector_centrality(max_iter=1000).asnumpy()
+    c = xgi.uniform_h_eigenvector_centrality(H, max_iter=1000)
+    c = np.array(list(c.values()))
     assert norm(c[1:] - c[1]) < 1e-4
-    assert abs(c[0] / c[1] - ratio(3, 5, kind="HEC")) < 1e-4
+    assert abs(c[0] / c[1] - _ratio(3, 5, kind="HEC")) < 1e-4
 
     H = xgi.sunflower(5, 1, 7)
-    c = H.nodes.h_eigenvector_centrality(max_iter=1000).asnumpy()
+    c = xgi.uniform_h_eigenvector_centrality(H, max_iter=1000)
+    c = np.array(list(c.values()))
     assert norm(c[1:] - c[1]) < 1e-4
-    assert abs(c[0] / c[1] - ratio(5, 7, kind="HEC")) < 1e-4
+    assert abs(c[0] / c[1] - _ratio(5, 7, kind="HEC")) < 1e-4
 
     with pytest.raises(XGIError):
         H = xgi.Hypergraph([[1, 2], [2, 3, 4]])
-        H.nodes.h_eigenvector_centrality.asnumpy()
+        xgi.uniform_h_eigenvector_centrality(H)
+
+    # non-convergence
+    with pytest.raises(XGIError):
+        H = xgi.Hypergraph([[1, 2], [2, 3, 4]])
+        xgi.uniform_h_eigenvector_centrality(H, max_iter=2)
 
 
 def test_node_edge_centrality():
@@ -105,6 +112,11 @@ def test_node_edge_centrality():
     c = H.edges.node_edge_centrality.asnumpy()
     assert abs(c[0] - c[1]) < 1e-6
 
+    H = xgi.load_xgi_data("email-enron").cleanup()
+    c = xgi.node_edge_centrality(H)
+    assert len(c[0]) == H.num_nodes
+    assert len(c[1]) == H.num_edges
+
 
 def test_line_vector_centrality():
     H = xgi.Hypergraph()
@@ -128,36 +140,6 @@ def test_line_vector_centrality():
         xgi.line_vector_centrality(H)
 
 
-def ratio(r, m, kind="CEC"):
-    """Generate the ratio between largest and second largest centralities
-    for the sunflower hypergraph with one core node.
-
-    Parameters
-    ----------
-    r : int
-        Number of petals
-    m : int
-        Size of edges
-    kind : str, default: "CEC"
-        "CEC" or "HEC"
-
-    Returns
-    -------
-    float
-        Ratio
-
-    References
-    ----------
-    Three Hypergraph Eigenvector Centralities,
-    Austin R. Benson,
-    https://doi.org/10.1137/18M1203031
-    """
-    if kind == "CEC":
-        return 2 * r * (m - 1) / (np.sqrt(m**2 + 4 * (m - 1) * (r - 1)) + m - 2)
-    elif kind == "HEC":
-        return r ** (1.0 / m)
-
-
 def test_katz_centrality(edgelist1, edgelist8):
     # test hypergraph with no edge
     H = xgi.Hypergraph()
@@ -195,3 +177,130 @@ def test_katz_centrality(edgelist1, edgelist8):
     }
     for n in c:
         assert np.allclose(c[n], expected_c[n])
+
+
+@pytest.mark.slow
+def test_h_eigenvector_centrality():
+    # test empty hypergraph
+    H = xgi.Hypergraph()
+    c = xgi.h_eigenvector_centrality(H)
+    assert c == dict()
+
+    # Test no edges
+    H.add_nodes_from([0, 1, 2])
+    hec = xgi.h_eigenvector_centrality(H)
+    for i in hec:
+        assert np.isnan(hec[i])
+
+    # test disconnected
+    H.add_edge([0, 1])
+    hec = xgi.h_eigenvector_centrality(H)
+    assert set(hec) == {0, 1, 2}
+    for i in hec:
+        assert np.isnan(hec[i])
+
+    H = xgi.sunflower(3, 1, 5)
+    c = xgi.h_eigenvector_centrality(H, max_iter=1000)
+    assert (
+        max([abs(c[0] / c[i + 1] - _ratio(3, 5, kind="HEC")) for i in range(12)]) < 1e-4
+    )
+
+    H = xgi.sunflower(5, 1, 7)
+    print(H.num_nodes)
+    c = xgi.h_eigenvector_centrality(H, max_iter=1000)
+    assert (
+        max([abs(c[0] / c[i + 1] - _ratio(5, 7, kind="HEC")) for i in range(29)]) < 1e-4
+    )
+
+    H = xgi.Hypergraph([[1, 2], [2, 3, 4]])
+    c = xgi.h_eigenvector_centrality(H)
+    true_c = {
+        1: 0.24458437592396465,
+        2: 0.3014043407819482,
+        3: 0.22700561916516002,
+        4: 0.22700566412892714,
+    }
+    for i in c:
+        assert np.allclose(c[i], true_c[i])
+
+    H = xgi.load_xgi_data("email-enron")
+    H.cleanup(relabel=False)
+    c = xgi.h_eigenvector_centrality(H)
+    assert sorted(c) == sorted(H.nodes)
+
+
+@pytest.mark.slow
+def test_z_eigenvector_centrality():
+    # test empty hypergraph
+    H = xgi.Hypergraph()
+    c = xgi.z_eigenvector_centrality(H)
+    assert c == dict()
+
+    # Test no edges
+    H.add_nodes_from([0, 1, 2])
+    hec = xgi.z_eigenvector_centrality(H)
+    for i in hec:
+        assert np.isnan(hec[i])
+
+    # test disconnected
+    H.add_edge([0, 1])
+    hec = xgi.z_eigenvector_centrality(H)
+    assert set(hec) == {0, 1, 2}
+    for i in hec:
+        assert np.isnan(hec[i])
+
+    H = xgi.sunflower(3, 1, 5)
+    c = H.nodes.z_eigenvector_centrality(max_iter=1000).asdict()
+    assert (
+        max([abs(c[0] / c[i + 1] - _ratio(3, 5, kind="ZEC")) for i in range(12)]) < 1e-4
+    )
+
+    H = xgi.sunflower(5, 1, 7)
+    print(H.num_nodes)
+    c = xgi.z_eigenvector_centrality(H, max_iter=1000)
+    assert (
+        max([abs(c[0] / c[i + 1] - _ratio(5, 7, kind="ZEC")) for i in range(29)]) < 1e-4
+    )
+
+    H = xgi.Hypergraph([[1, 2], [2, 3, 4]])
+    c = xgi.z_eigenvector_centrality(H, max_iter=10000)
+    true_c = {
+        1: 0.45497398635982933,
+        2: 0.45900452108663403,
+        3: 0.04301074627676834,
+        4: 0.04301074627676829,
+    }
+    for i in c:
+        assert np.allclose(c[i], true_c[i])
+
+
+def _ratio(r, m, kind="CEC"):
+    """Generate the _ratio between largest and second largest centralities
+    for the sunflower hypergraph with one core node.
+
+    Parameters
+    ----------
+    r : int
+        Number of petals
+    m : int
+        Size of edges
+    kind : str, default: "CEC"
+        "CEC" or "HEC"
+
+    Returns
+    -------
+    float
+        Ratio
+
+    References
+    ----------
+    Three Hypergraph Eigenvector Centralities,
+    Austin R. Benson,
+    https://doi.org/10.1137/18M1203031
+    """
+    if kind == "CEC":
+        return 2 * r * (m - 1) / (np.sqrt(m**2 + 4 * (m - 1) * (r - 1)) + m - 2)
+    elif kind == "HEC":
+        return r ** (1.0 / m)
+    elif kind == "ZEC":
+        return r**0.5