diff --git a/2022-round-1/arpitadash/nx_dev_test_output.txt b/2022-round-1/arpitadash/nx_dev_test_output.txt
new file mode 100644
index 0000000..a5e65aa
--- /dev/null
+++ b/2022-round-1/arpitadash/nx_dev_test_output.txt
@@ -0,0 +1,380 @@
+============================= test session starts =============================
+platform win32 -- Python 3.10.2, pytest-7.1.1, pluggy-1.0.0
+rootdir: D:\Arpita\Outreachy\networkx\networkx
+plugins: cov-3.0.0
+collected 4891 items / 3 skipped
+
+networkx\algorithms\approximation\tests\test_approx_clust_coeff.py ..... [  0%]
+.                                                                        [  0%]
+networkx\algorithms\approximation\tests\test_clique.py ........          [  0%]
+networkx\algorithms\approximation\tests\test_connectivity.py ........... [  0%]
+.......                                                                  [  0%]
+networkx\algorithms\approximation\tests\test_distance_measures.py ...... [  0%]
+..                                                                       [  0%]
+networkx\algorithms\approximation\tests\test_dominating_set.py ...       [  0%]
+networkx\algorithms\approximation\tests\test_kcomponents.py ............ [  1%]
+....                                                                     [  1%]
+networkx\algorithms\approximation\tests\test_matching.py .               [  1%]
+networkx\algorithms\approximation\tests\test_maxcut.py .....             [  1%]
+networkx\algorithms\approximation\tests\test_ramsey.py .                 [  1%]
+networkx\algorithms\approximation\tests\test_steinertree.py ....         [  1%]
+networkx\algorithms\approximation\tests\test_traveling_salesman.py ..... [  1%]
+...............................s......s.                                 [  2%]
+networkx\algorithms\approximation\tests\test_treewidth.py ............   [  2%]
+networkx\algorithms\approximation\tests\test_vertex_cover.py ....        [  2%]
+networkx\algorithms\assortativity\tests\test_connectivity.py ..........  [  2%]
+networkx\algorithms\assortativity\tests\test_correlation.py ............ [  3%]
+.......                                                                  [  3%]
+networkx\algorithms\assortativity\tests\test_mixing.py ................. [  3%]
+..                                                                       [  3%]
+networkx\algorithms\assortativity\tests\test_neighbor_degree.py ......   [  3%]
+networkx\algorithms\assortativity\tests\test_pairs.py ...........        [  4%]
+networkx\algorithms\bipartite\tests\test_basic.py ...............        [  4%]
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+networkx\algorithms\bipartite\tests\test_cluster.py .........            [  4%]
+networkx\algorithms\bipartite\tests\test_covering.py ....                [  4%]
+networkx\algorithms\bipartite\tests\test_edgelist.py ..............      [  4%]
+networkx\algorithms\bipartite\tests\test_generators.py ..........        [  5%]
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+.                                                                        [  5%]
+networkx\algorithms\bipartite\tests\test_matrix.py ...........           [  5%]
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+networkx\algorithms\centrality\tests\test_betweenness_centrality.py .... [  6%]
+.....................................                                    [  7%]
+networkx\algorithms\centrality\tests\test_betweenness_centrality_subset.py . [  7%]
+................                                                         [  7%]
+networkx\algorithms\centrality\tests\test_closeness_centrality.py ...... [  7%]
+.......                                                                  [  7%]
+networkx\algorithms\centrality\tests\test_current_flow_betweenness_centrality.py . [  7%]
+...............                                                          [  8%]
+networkx\algorithms\centrality\tests\test_current_flow_betweenness_centrality_subset.py . [  8%]
+........                                                                 [  8%]
+networkx\algorithms\centrality\tests\test_current_flow_closeness.py ...  [  8%]
+networkx\algorithms\centrality\tests\test_degree_centrality.py .......   [  8%]
+networkx\algorithms\centrality\tests\test_dispersion.py ...              [  8%]
+networkx\algorithms\centrality\tests\test_eigenvector_centrality.py .... [  8%]
+........                                                                 [  8%]
+networkx\algorithms\centrality\tests\test_group.py ..................... [  9%]
+...                                                                      [  9%]
+networkx\algorithms\centrality\tests\test_harmonic_centrality.py ....... [  9%]
+......                                                                   [  9%]
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+...............                                                          [ 10%]
+networkx\algorithms\centrality\tests\test_load_centrality.py ........... [ 10%]
+......                                                                   [ 10%]
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+networkx\algorithms\centrality\tests\test_reaching.py ..............     [ 10%]
+networkx\algorithms\centrality\tests\test_second_order_centrality.py ... [ 10%]
+....                                                                     [ 10%]
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+networkx\algorithms\centrality\tests\test_trophic.py ..........          [ 11%]
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+networkx\algorithms\coloring\tests\test_coloring.py ................     [ 11%]
+networkx\algorithms\community\tests\test_asyn_fluid.py .....             [ 11%]
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+networkx\algorithms\community\tests\test_kernighan_lin.py ........       [ 12%]
+networkx\algorithms\community\tests\test_label_propagation.py .......... [ 12%]
+.                                                                        [ 12%]
+networkx\algorithms\community\tests\test_louvain.py ........             [ 12%]
+networkx\algorithms\community\tests\test_lukes.py ....                   [ 12%]
+networkx\algorithms\community\tests\test_modularity_max.py ............. [ 12%]
+....                                                                     [ 12%]
+networkx\algorithms\community\tests\test_quality.py .......              [ 13%]
+networkx\algorithms\community\tests\test_utils.py ....                   [ 13%]
+networkx\algorithms\components\tests\test_attracting.py ....             [ 13%]
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+networkx\algorithms\components\tests\test_strongly_connected.py ........ [ 14%]
+......                                                                   [ 14%]
+networkx\algorithms\components\tests\test_weakly_connected.py ......     [ 14%]
+networkx\algorithms\connectivity\tests\test_connectivity.py ............ [ 14%]
+......................                                                   [ 14%]
+networkx\algorithms\connectivity\tests\test_cuts.py .................... [ 15%]
+.                                                                        [ 15%]
+networkx\algorithms\connectivity\tests\test_disjoint_paths.py .......... [ 15%]
+........                                                                 [ 15%]
+networkx\algorithms\connectivity\tests\test_edge_augmentation.py ....... [ 15%]
+.............                                                            [ 16%]
+networkx\algorithms\connectivity\tests\test_edge_kcomponents.py ........ [ 16%]
+.............                                                            [ 16%]
+networkx\algorithms\connectivity\tests\test_kcomponents.py .sss......    [ 16%]
+networkx\algorithms\connectivity\tests\test_kcutsets.py s........s.....  [ 17%]
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+networkx\algorithms\flow\tests\test_gomory_hu.py ....s....               [ 17%]
+networkx\algorithms\flow\tests\test_maxflow.py ......................... [ 17%]
+..                                                                       [ 17%]
+networkx\algorithms\flow\tests\test_maxflow_large_graph.py ...s..        [ 18%]
+networkx\algorithms\flow\tests\test_mincost.py ...................       [ 18%]
+networkx\algorithms\flow\tests\test_networksimplex.py .................. [ 18%]
+....                                                                     [ 18%]
+networkx\algorithms\isomorphism\tests\test_ismags.py ..........          [ 19%]
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+networkx\algorithms\isomorphism\tests\test_isomorphvf2.py .............. [ 19%]
+.                                                                        [ 19%]
+networkx\algorithms\isomorphism\tests\test_match_helpers.py ..           [ 19%]
+networkx\algorithms\isomorphism\tests\test_temporalisomorphvf2.py ...... [ 19%]
+......                                                                   [ 19%]
+networkx\algorithms\isomorphism\tests\test_tree_isomorphism.py .....     [ 19%]
+networkx\algorithms\isomorphism\tests\test_vf2userfunc.py .............. [ 20%]
+..............                                                           [ 20%]
+networkx\algorithms\link_analysis\tests\test_hits.py ........            [ 20%]
+networkx\algorithms\link_analysis\tests\test_pagerank.py ............... [ 20%]
+.....................................                                    [ 21%]
+networkx\algorithms\minors\tests\test_contraction.py ................... [ 22%]
+............                                                             [ 22%]
+networkx\algorithms\operators\tests\test_all.py ..................       [ 22%]
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+.......                                                                  [ 23%]
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+networkx\algorithms\shortest_paths\tests\test_astar.py .............     [ 24%]
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+.......                                                                  [ 24%]
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+                                                                         [ 25%]
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+.......................................                                  [ 26%]
+networkx\algorithms\tests\test_asteroidal.py .                           [ 26%]
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+networkx\algorithms\tests\test_bridges.py ......                         [ 26%]
+networkx\algorithms\tests\test_chains.py ....                            [ 26%]
+networkx\algorithms\tests\test_chordal.py ..........                     [ 26%]
+networkx\algorithms\tests\test_clique.py ..............                  [ 27%]
+networkx\algorithms\tests\test_cluster.py .............................. [ 27%]
+..........                                                               [ 27%]
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+...                                                                      [ 29%]
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+networkx\algorithms\tests\test_dag.py .................................. [ 30%]
+...................                                                      [ 30%]
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+.............                                                            [ 31%]
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+                                                                         [ 33%]
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+networkx\algorithms\tests\test_hybrid.py ..                              [ 33%]
+networkx\algorithms\tests\test_isolate.py ...                            [ 33%]
+networkx\algorithms\tests\test_link_prediction.py ...................... [ 34%]
+...................................................                      [ 35%]
+networkx\algorithms\tests\test_lowest_common_ancestors.py .............. [ 35%]
+...........                                                              [ 35%]
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+...............                                                          [ 36%]
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+networkx\algorithms\tests\test_mis.py ........                           [ 37%]
+networkx\algorithms\tests\test_moral.py .                                [ 37%]
+networkx\algorithms\tests\test_node_classification.py ...............    [ 37%]
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+networkx\algorithms\tests\test_non_randomness.py ......                  [ 37%]
+networkx\algorithms\tests\test_planar_drawing.py ............            [ 37%]
+networkx\algorithms\tests\test_planarity.py ............................ [ 38%]
+..                                                                       [ 38%]
+networkx\algorithms\tests\test_polynomials.py ........                   [ 38%]
+networkx\algorithms\tests\test_reciprocity.py .....                      [ 38%]
+networkx\algorithms\tests\test_regular.py .............                  [ 38%]
+networkx\algorithms\tests\test_richclub.py ........                      [ 39%]
+networkx\algorithms\tests\test_similarity.py ........................... [ 39%]
+.................                                                        [ 39%]
+networkx\algorithms\tests\test_simple_paths.py ......................... [ 40%]
+................................................                         [ 41%]
+networkx\algorithms\tests\test_smallworld.py ....                        [ 41%]
+networkx\algorithms\tests\test_smetric.py ..                             [ 41%]
+networkx\algorithms\tests\test_sparsifiers.py .......                    [ 41%]
+networkx\algorithms\tests\test_structuralholes.py ............           [ 41%]
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+networkx\algorithms\tests\test_swap.py .............                     [ 42%]
+networkx\algorithms\tests\test_threshold.py ..................           [ 42%]
+networkx\algorithms\tests\test_tournament.py .....................       [ 43%]
+networkx\algorithms\tests\test_triads.py ........                        [ 43%]
+networkx\algorithms\tests\test_vitality.py ......                        [ 43%]
+networkx\algorithms\tests\test_voronoi.py ..........                     [ 43%]
+networkx\algorithms\tests\test_wiener.py ....                            [ 43%]
+networkx\algorithms\traversal\tests\test_beamsearch.py ..                [ 44%]
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+networkx\algorithms\traversal\tests\test_edgedfs.py ...............      [ 45%]
+networkx\algorithms\tree\tests\test_branchings.py ...................... [ 45%]
+.....                                                                    [ 45%]
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+networkx\algorithms\tree\tests\test_decomposition.py .....               [ 46%]
+networkx\algorithms\tree\tests\test_mst.py ............................. [ 46%]
+.................                                                        [ 47%]
+networkx\algorithms\tree\tests\test_operations.py ...                    [ 47%]
+networkx\algorithms\tree\tests\test_recognition.py ..................... [ 47%]
+....                                                                     [ 47%]
+networkx\classes\tests\test_coreviews.py ............................... [ 48%]
+..........................                                               [ 48%]
+networkx\classes\tests\test_digraph.py ................................. [ 49%]
+...............................................                          [ 50%]
+networkx\classes\tests\test_digraph_historical.py ...................... [ 50%]
+....................                                                     [ 51%]
+networkx\classes\tests\test_filters.py ...........                       [ 51%]
+networkx\classes\tests\test_function.py ................................ [ 52%]
+....................................                                     [ 53%]
+networkx\classes\tests\test_graph.py ................................... [ 53%]
+...........................                                              [ 54%]
+networkx\classes\tests\test_graph_historical.py ........................ [ 54%]
+..........                                                               [ 54%]
+networkx\classes\tests\test_graphviews.py .............................. [ 55%]
+.....                                                                    [ 55%]
+networkx\classes\tests\test_multidigraph.py ............................ [ 56%]
+.................................................................        [ 57%]
+networkx\classes\tests\test_multigraph.py .............................. [ 58%]
+................................................                         [ 59%]
+networkx\classes\tests\test_ordered.py .....                             [ 59%]
+networkx\classes\tests\test_reportviews.py ............................. [ 59%]
+........................................................................ [ 61%]
+........................................................................ [ 62%]
+................................................................         [ 64%]
+networkx\classes\tests\test_special.py ................................. [ 64%]
+........................................................................ [ 66%]
+........................................................................ [ 67%]
+........................................................................ [ 69%]
+........................................................................ [ 70%]
+........................................................................ [ 72%]
+........................................................................ [ 73%]
+........................................................................ [ 75%]
+........................................................................ [ 76%]
+...                                                                      [ 76%]
+networkx\classes\tests\test_subgraphviews.py ........................... [ 77%]
+.....                                                                    [ 77%]
+networkx\drawing\tests\test_layout.py ..........................         [ 77%]
+networkx\drawing\tests\test_pylab.py ................................... [ 78%]
+........................................................                 [ 79%]
+networkx\generators\tests\test_atlas.py ........                         [ 79%]
+networkx\generators\tests\test_classic.py .............................. [ 80%]
+                                                                         [ 80%]
+networkx\generators\tests\test_cographs.py .                             [ 80%]
+networkx\generators\tests\test_community.py ................             [ 80%]
+networkx\generators\tests\test_degree_seq.py ...................         [ 81%]
+networkx\generators\tests\test_directed.py ........                      [ 81%]
+networkx\generators\tests\test_duplication.py .......                    [ 81%]
+networkx\generators\tests\test_ego.py ..                                 [ 81%]
+networkx\generators\tests\test_expanders.py ....                         [ 81%]
+networkx\generators\tests\test_geometric.py .......................      [ 82%]
+networkx\generators\tests\test_harary_graph.py ..                        [ 82%]
+networkx\generators\tests\test_internet_as_graphs.py .....               [ 82%]
+networkx\generators\tests\test_intersection.py ....                      [ 82%]
+networkx\generators\tests\test_interval_graph.py ........                [ 82%]
+networkx\generators\tests\test_joint_degree_seq.py ....                  [ 82%]
+networkx\generators\tests\test_lattice.py ......................         [ 83%]
+networkx\generators\tests\test_line.py ..............................    [ 83%]
+networkx\generators\tests\test_mycielski.py ...                          [ 83%]
+networkx\generators\tests\test_nonisomorphic_trees.py .....              [ 83%]
+networkx\generators\tests\test_random_clustered.py ....                  [ 83%]
+networkx\generators\tests\test_random_graphs.py ........................ [ 84%]
+.......................................                                  [ 85%]
+networkx\generators\tests\test_small.py ................................ [ 85%]
+.......                                                                  [ 85%]
+networkx\generators\tests\test_spectral_graph_forge.py .                 [ 85%]
+networkx\generators\tests\test_stochastic.py ......                      [ 86%]
+networkx\generators\tests\test_sudoku.py ......                          [ 86%]
+networkx\generators\tests\test_trees.py .......                          [ 86%]
+networkx\generators\tests\test_triads.py ..                              [ 86%]
+networkx\linalg\tests\test_algebraic_connectivity.py ................... [ 86%]
+....................................................................     [ 88%]
+networkx\linalg\tests\test_attrmatrix.py .....                           [ 88%]
+networkx\linalg\tests\test_bethehessian.py .                             [ 88%]
+networkx\linalg\tests\test_graphmatrix.py ....                           [ 88%]
+networkx\linalg\tests\test_laplacian.py ....                             [ 88%]
+networkx\linalg\tests\test_modularity.py ...                             [ 88%]
+networkx\linalg\tests\test_spectrum.py .....                             [ 88%]
+networkx\readwrite\json_graph\tests\test_adjacency.py ......             [ 88%]
+networkx\readwrite\json_graph\tests\test_cytoscape.py ........           [ 88%]
+networkx\readwrite\json_graph\tests\test_jit.py .....                    [ 89%]
+networkx\readwrite\json_graph\tests\test_node_link.py .........          [ 89%]
+networkx\readwrite\json_graph\tests\test_tree.py ....                    [ 89%]
+networkx\readwrite\tests\test_adjlist.py ..................              [ 89%]
+networkx\readwrite\tests\test_edgelist.py ..........................     [ 90%]
+networkx\readwrite\tests\test_getattr_nxyaml_removal.py ....             [ 90%]
+networkx\readwrite\tests\test_gexf.py .....................              [ 90%]
+networkx\readwrite\tests\test_gml.py .....................               [ 91%]
+networkx\readwrite\tests\test_gpickle.py ..                              [ 91%]
+networkx\readwrite\tests\test_graph6.py ...............                  [ 91%]
+networkx\readwrite\tests\test_graphml.py ..................sssssssssssss [ 92%]
+ssssssssssssssssssssssssssssss                                           [ 92%]
+networkx\readwrite\tests\test_leda.py ..                                 [ 92%]
+networkx\readwrite\tests\test_p2g.py ...                                 [ 92%]
+networkx\readwrite\tests\test_pajek.py ........                          [ 93%]
+networkx\readwrite\tests\test_sparse6.py ................                [ 93%]
+networkx\readwrite\tests\test_text.py .......                            [ 93%]
+networkx\testing\tests\test_utils.py .....................               [ 93%]
+networkx\tests\test_all_random_functions.py s                            [ 93%]
+networkx\tests\test_convert.py ...............                           [ 94%]
+networkx\tests\test_convert_numpy.py ................................... [ 94%]
+........................................                                 [ 95%]
+networkx\tests\test_convert_pandas.py ......................             [ 96%]
+networkx\tests\test_convert_scipy.py .....................               [ 96%]
+networkx\tests\test_exceptions.py .......                                [ 96%]
+networkx\tests\test_import.py ..                                         [ 96%]
+networkx\tests\test_lazy_imports.py ....                                 [ 96%]
+networkx\tests\test_relabel.py .......................                   [ 97%]
+networkx\utils\tests\test__init.py .                                     [ 97%]
+networkx\utils\tests\test_contextmanager.py .                            [ 97%]
+networkx\utils\tests\test_decorators.py ................................ [ 98%]
+...                                                                      [ 98%]
+networkx\utils\tests\test_heaps.py ..                                    [ 98%]
+networkx\utils\tests\test_mapped_queue.py .............................. [ 98%]
+..........                                                               [ 98%]
+networkx\utils\tests\test_misc.py ...................................... [ 99%]
+                                                                         [ 99%]
+networkx\utils\tests\test_random_sequence.py ....                        [ 99%]
+networkx\utils\tests\test_rcm.py ..                                      [ 99%]
+networkx\utils\tests\test_unionfind.py .....                             [100%]
+
+============================== warnings summary ===============================
+networkx\drawing\tests\test_pylab.py:419
+  D:\Arpita\Outreachy\networkx\networkx\networkx\drawing\tests\test_pylab.py:419: PytestUnknownMarkWarning: Unknown pytest.mark.mpl_image_compare - is this a typo?  You can register custom marks to avoid this warning - for details, see https://docs.pytest.org/en/stable/how-to/mark.html
+    @pytest.mark.mpl_image_compare
+
+networkx\utils\decorators.py:292
+  D:\Arpita\Outreachy\networkx\networkx\networkx\utils\decorators.py:292: DeprecationWarning: preserve_random_state is deprecated and will be removed in 3.0.
+    warnings.warn(msg, DeprecationWarning)
+
+networkx/algorithms/approximation/tests/test_traveling_salesman.py::test_held_karp_ascent
+networkx/algorithms/approximation/tests/test_traveling_salesman.py::test_ascent_fractional_solution
+networkx/algorithms/approximation/tests/test_traveling_salesman.py::test_ascent_method_asymmetric
+networkx/algorithms/approximation/tests/test_traveling_salesman.py::test_held_karp_ascent_asymmetric_3
+networkx/algorithms/approximation/tests/test_traveling_salesman.py::test_held_karp_ascent_fractional_asymmetric
+networkx/algorithms/approximation/tests/test_traveling_salesman.py::test_asadpour_tsp
+  D:\Arpita\Outreachy\networkx\networkx\networkx\algorithms\approximation\traveling_salesman.py:679: OptimizeWarning: A_eq does not appear to be of full row rank. To improve performance, check the problem formulation for redundant equality constraints.
+    program_result = optimize.linprog(c, A_eq=a_eq, b_eq=b_eq)
+
+networkx/classes/tests/test_ordered.py::TestOrderedFeatures::test_subgraph_order
+  D:\Arpita\Outreachy\networkx\networkx\networkx\classes\tests\test_ordered.py:22: DeprecationWarning: OrderedDiGraph is deprecated and will be removed in version 3.0.
+  Use `DiGraph` instead, which guarantees order is preserved for
+  Python >= 3.7
+  
+    cls.G = nx.OrderedDiGraph()
+
+networkx/linalg/tests/test_algebraic_connectivity.py::TestSpectralOrdering::test_cycle[lobpcg-False-expected_order0]
+  D:\Arpita\Outreachy\networkx\networkx\networkx\linalg\algebraicconnectivity.py:301: UserWarning: Exited at iteration 10 with accuracies 
+  [0.02743716]
+  not reaching the requested tolerance 1e-08.
+    sigma, X = sp.sparse.linalg.lobpcg(
+
+networkx/linalg/tests/test_algebraic_connectivity.py::TestSpectralOrdering::test_cycle[lobpcg-True-expected_order1]
+  D:\Arpita\Outreachy\networkx\networkx\networkx\linalg\algebraicconnectivity.py:301: UserWarning: Exited at iteration 10 with accuracies 
+  [0.00056623]
+  not reaching the requested tolerance 1e-08.
+    sigma, X = sp.sparse.linalg.lobpcg(
+
+-- Docs: https://docs.pytest.org/en/stable/how-to/capture-warnings.html
+========== 4838 passed, 56 skipped, 11 warnings in 219.55s (0:03:39) ==========
diff --git a/2022-round-1/arpitadash/nx_notebook.ipynb b/2022-round-1/arpitadash/nx_notebook.ipynb
new file mode 100644
index 0000000..bd95c86
--- /dev/null
+++ b/2022-round-1/arpitadash/nx_notebook.ipynb
@@ -0,0 +1,252 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "3a926d35",
+   "metadata": {},
+   "source": [
+    "# Tasks\n",
+    "\n",
+    "* Create a random erdos-renyi graph with 100 nodes and a edge probability of 0.3\n",
+    "* Plot the degree_centrality distribution (a histogram of the degree centrality values).\n",
+    "* Change the edge probability of the erdos-reyni graph to 0.6 and plot the degree centrality distribution again.\n",
+    "* Infer the changes in the plots, why does the degree centrality distribution change. Create a markdown cell in the jupyter notebook and write what you can infer from the plots.\n",
+    "* Create a random barabasi_albert_graph with 100 nodes and attach 3 edges to a new node in the graph (m=3).\n",
+    "* Plot the degree_centrality distribution (a histogram of the degree histogram).\n",
+    "* Infer the changes in the plots, why does the degree centrality distribution change between these 2 random graph generators \n",
+    "* Create a markdown cell in the jupyter notebook and write what you can infer from the plots."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3ab15c61",
+   "metadata": {},
+   "source": [
+    "# Import Libraries"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "934a2d7a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import networkx as nx\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0033437",
+   "metadata": {},
+   "source": [
+    "## Plotting graphs"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fb946843",
+   "metadata": {},
+   "source": [
+    "Creating a function that plots the histogram of the degree distribution in the graph. First, we store the degree of all nodes. Then, using the matplotlib histogram function, we plot the histogram distribution."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "id": "5fbb376a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def create_and_plot_graph(G,prob='NA'):\n",
+    "    deg = [d for n,d in G.degree()]\n",
+    "    first_edge, last_edge = np.min(deg), np.max(deg)\n",
+    "    n, bins, patches = plt.hist(x=deg, bins=20, color='#0504aa', alpha=0.7, rwidth=0.75)\n",
+    "#     plt.xlim([first_edge-1, last_edge+1])\n",
+    "    plt.xlim([0,100])\n",
+    "    plt.title(str(G)+' probability: '+str(prob))\n",
+    "    plt.ylabel('# of nodes')\n",
+    "    plt.xlabel('Degree')\n",
+    "    plt.grid('on')\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d3e429ff",
+   "metadata": {},
+   "source": [
+    "## Erdos-Renyi Graph"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c4fd6a26",
+   "metadata": {},
+   "source": [
+    "Erdos-Renyi algorithm is a random graph generator. The graphs generated are chosen only if the edge probability is higher than a certain specified value. Higher the probability, more the number of edges. \n",
+    "$G(n,p)$ is the graph where $n$ is the number of nodes in the graph, and $p$ is the edge probability."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "id": "89a41c0b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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mZqUcIMzMrJQDhJmZlXKAMDOzUg4QZmZWqmkBQtI3JD0s6baStFMkhaStmpW/mZmNTzN7EOcCh1RPlLQjcBDwhybmbWZm49S0ABER1wCPlSR9ETgViGblbWZm49fSexCSDgfuj4hftjJfMzNbd4po3om8pFnAoojYXdLGwFXAQRGxUtI9wJyIWFZj2fnAfIDe3t69BwYGmlbOyWR4eJienp52F6MjuC5G1KuLJUuGAZg9uzvqyu1ixNy5cxdHxJyxLt/KAPFS4CfAkzl5B+AB4JUR8VC99fT19cXQ0FDTyjmZDA4O0t/f3+5idATXxYh6dVF51ffChfu3sETt43YxQtK4AsT0iSxMPRHxa2DryvhoPQgzM2uvZj7mehFwPdAnaamkE5uVl5mZTbym9SAi4qhR0mc1K28zMxs/f5PazMxKOUCYmVkpBwgzMyvlAGFmZqUcIMzMrJQDhJmZlXKAMDOzUg4QZmZWygHCbBKZN++6Ne9WMms2BwgzMyvlAGFmZqUcIMzMrJQDhJmZlXKAMDOzUg4QZmZWygHCzMxKOUCYmVkpBwgzMyvlAGFmZqWaFiAkfUPSw5JuK0z7vKS7JP1K0mWSZjYrfzMzG59m9iDOBQ6pmnYlsHtEvAz4DfDRJuZvZmbj0LQAERHXAI9VTftRRKzOozcAOzQrfzMzGx9FRPNWLs0CFkXE7iVplwMXR8QFNZadD8wH6O3t3XtgYKBp5ZxMhoeH6enpaXcxOkI31sWSJcMAzJ699nbXq4tay0xV3dguapk7d+7iiJgz1uXbEiAk/T0wB/jLaKAAfX19MTQ01JxCTjKDg4P09/e3uxgdoRvrovKq74UL919rer26qLXMVNWN7aIWSeMKENMnsjCNkHQ8cBhwQCPBwczM2qOlAULSIcCpwOsi4slW5m1mZuummY+5XgRcD/RJWirpRODLwCbAlZJulfTVZuVvZmbj07QeREQcVTJ5QbPyMzOzieVvUpuZWSkHCDMzK+UAYWZmpRwgzMyslAOEmZmVcoAwM7NSDhBmZlbKAcLMzEo5QJiZWSkHCDMzK+UAYWZmpRwgzMyslAOEmZmVcoAwM7NSDhBmZlbKAcLMzEo5QJiZWSkHCDMzK+UAYWZmpZoWICR9Q9LDkm4rTNtC0pWSfpv/b96s/M3MbHya2YM4FzikatppwE8i4oXAT/K4mZl1oKYFiIi4BnisavLhwHl5+DxgXrPyNzOz8VFENG/l0ixgUUTsnsdXRMTMPCxgeWW8ZNn5wHyA3t7evQcGBppWzslkeHiYnp6edhejI3RjXSxZMgzA7Nlrb3e9uqi1zFTVje2ilrlz5y6OiDljXb5tASKPL4+IUe9D9PX1xdDQUNPKOZkMDg7S39/f7mJ0hG6si3nzrgNg4cL915pery5qLTNVdWO7qEXSuAJEq59i+qOkbQHy/4dbnL+ZmTWo1QHiB8Bxefg44Pstzt/MzBo0aoCQdLKkTZUskHSzpIMaWO4i4HqgT9JSSScCnwPeIOm3wIF53MzMOtD0BuZ5V0R8SdLBwObAscD5wI/qLRQRR9VIOmDdimhmZu3QyCUm5f+HAudHxO2FaWZmNkU1EiAWS/oRKUBcIWkT4NnmFsvMzNqtkUtMJwJ7AHdHxJOStgROaGqpzMys7RrpQQSwG/DBPD4D2LBpJTIzs47QSID4CrAvULnp/ATw700rkZmZdYRGLjG9KiL2knQLQEQsl7RBk8tlZmZt1kgP4mlJ00iXmpDUi29Sm5lNeY0EiLOAy4CtJZ0JXAd8tqmlMjOzthv1ElNEXChpMekLbgLmRcSdTS+ZmZm1Vc0AIWmLwujDwEXFtIio/q0HMzObQur1IBaT7jsIeAGwPA/PBP4A7NzswpmZWfvUvAcRETtHxC7Aj4E3R8RWEbElcBijvIfJzMwmv0ZuUu8TEf9VGYmIHwKvbl6RzMysEzTyPYgHJJ0OXJDHjwYeaF6RzMysEzTSgzgK6CU96noZsDUj36o2M7MpqpHHXB8DTs5vcY2IGG5+sczMrN0a+UW5l+bXbNwG3C5psaTdm180MzNrp0YuMX0N+LuI2CkidgJOAc5pbrHMzKzdGgkQMyLiqspIRAySXvk9ZpI+JOl2SbdJukiSXx9uZtZhGgkQd0v6uKRZ+e904O6xZihpe9JvS8yJiN2BacCRY12fmZk1RyMB4l2kp5guzX+9edp4TAc2kjQd2Bg/Nmtm1nEUEa3PVDoZOBP4E/CjiDi6ZJ75wHyA3t7evQcGBlpbyA41PDxMT09Pu4vREbqxLpYsSQ8Rzp7ds9ZwvbooztcNurFd1DJ37tzFETFnrMuPGiAkvQj4MDCLwmOxEfH6MWUobQ58D3gHsAL4LnBJRFxQa5m+vr4YGhoaS3ZTzuDgIP39/e0uRkfoxrqYN+86ABYu3H+t4Xp1UZyvG3Rju6hF0rgCRCPfpP4u8FXg68AzY82o4EDg9xHxCICkS0mv7qgZIMzMrPUaCRCrI+LsCczzD8A+kjYmXWI6ALhpAtdvZmYToJGb1JdLOknStpK2qPyNNcOIuBG4BLgZ+HUug79XYWbWYRrpQRyX///fwrQAdhlrphHxSeCTY13ezMyar5F3MfmHgczMulAjl5jMzKwLOUCYmVmpmgFC0n75//NaVxwzM+sU9XoQZ+X/17eiIGZm1lnq3aR+WtI5wPaSzqpOjIgPNq9YZmbWbvUCxGGkbz0fDCxuTXHMzKxT1AwQEbEM+I6kOyPily0sk5mZdYBGvij3qKTLgP3y+LXAyRGxtHnFMusurXqhXiWfVuRlk18jj7l+E/gBsF3+uzxPMzOzKayRALF1RHwzIlbnv3NJPxpkZmZTWCMBYpmkYyRNy3/HAI82u2BmZtZejf7k6NuBh4AHgSOAE5pZKDMza79GXtZ3L/CWFpTFzMw6iN/FZGZmpRwgzMyslAOEmZmVGjVASDq9MOw3u5qZdYl6r/v+iKR9SU8tVfjNrmZmXaJeD+Iu4G3ALpKulfQfwJaS+sabqaSZki6RdJekO3MgMjOzDlIvQKwAPgb8DugHvpSnnybpZ+PM90vAf0fEi4GXA3eOc31mZjbB6n0P4mDgE8Bs4AvAr4BVETGuL8lJ2gx4LXA8QEQ8BTw1nnWamdnEU0TUn0H6JXAisBdwJjAELI+IN48pQ2kP4BzgDlLvYTHp7bCrquabD8wH6O3t3XtgYGAs2U05w8PD9PT0tLsYHWEq1cWSJcMAzJ7ds9Zwo/MtW7aSlSunlS5XtkwjeU1WU6ldjNfcuXMXR8ScsS7fSID454g4NQ/fEhF7Stoq/17EumcozQFuAPaLiBslfQl4PCI+XmuZvr6+GBoaGkt2U87g4CD9/f3tLkZHmEp1UXzdd71Xf9eab8GCRVx++czS5cqWaSSvyWoqtYvxkjSuADHqY66V4JAdn6eNKThkS4GlEXFjHr+E1DsxM7MOsk5flJuIX5aLiIeA+wpPQx1AutxkZmYdpJFflGuGvwEulLQBcDd+O6yZWcdpS4CIiFuBMV8XMzOz5vO7mMzMrJQDhJmZlXKAMDOzUg4QZmZWygHCzMxKOUCYmVkpBwgzMyvlAGFmZqXa9U1qM2ui8b6Er/qlftad3IMwM7NSDhBmZlbKAcLMzEo5QJiZWSkHCDMzK+UAYWZmpRwgzMyslAOEmZmVcoAwM7NSbQsQkqZJukXSonaVwczMamtnD+Jk4M425m9mZnW0JUBI2gF4E/D1duRvZmaja1cP4l+BU4Fn25S/mZmNQhHR2gylw4BDI+IkSf3AhyPisJL55gPzAXp7e/ceGBhoaTk71fDwMD09Pe0uRkeYzHWxZMnwmuHZs3vWjNcaHm2+ZctWsnLltAlbX/V8k8lkbhcTbe7cuYsjYs5Yl29HgPhH4FhgNbAhsClwaUQcU2uZvr6+GBoaalEJO9vg4CD9/f3tLkZHmMx1Uf067eLrucuGR5tvwYJFXH75zAlb32R+3fdkbhcTTdK4AkTLLzFFxEcjYoeImAUcCfy0XnAwM7P28PcgzMysVFt/US4iBoHBdpbBzMzKuQdhZmalHCDMzKyUA4SZmZVygDAzs1IOEGZmVsoBwszMSjlAmJlZKQcIMzMr1dYvyplNZZP5fUZm4B6EmZnV4ABhZmalHCDMzKyUA4SZmZVygDAzs1IOEGZmVsoBwszMSjlAmJlZKQcIMzMr5QBhZmalWh4gJO0o6SpJd0i6XdLJrS6DmZmNrh3vYloNnBIRN0vaBFgs6cqIuKMNZTEzsxpa3oOIiAcj4uY8/ARwJ7B9q8thZmb1KSLal7k0C7gG2D0iHq9Kmw/MB+jt7d17YGCg9QXsQMPDw/T09LS7GB2h0+tiyZLhNcOzZ/esGS8O10tbl/mWLVvJypXTJmx91fPV265O0+ntopXmzp27OCLmjHX5tgUIST3A1cCZEXFpvXn7+vpiaGioNQXrcIODg/T397e7GB2h0+ui+nXflfHicL20dZlvwYJFXH75zAlbX71XlXf6a8w7vV20kqRxBYi2PMUkaX3ge8CFowUHMzNrj3Y8xSRgAXBnRHyh1fmbmVlj2tGD2A84Fni9pFvz36FtKIeZmdXR8sdcI+I6QK3O18zM1o2/SW1mZqUcIMzMrJQDhJmZlXKAMDOzUg4QZmZWygHCzMxKOUCYmVkpBwgzMyvVjt+DMJvU6r3wbqrqhm2053IPwszMSjlAmJlZKQcIMzMr5QBhZmalHCDMzKyUA4SZmZVygDAzs1IOEGZmVsoBwszMSjlAmJlZqbYECEmHSBqS9DtJp7WjDGZmVl/LA4SkacC/A28EdgOOkrRbq8thZmb1taMH8UrgdxFxd0Q8BXwHOLwN5TAzszra8TbX7YH7CuNLgVdVzyRpPjA/j/5Z0m0tKNtksBWwrN2F6BBtrwupfHhd5quVto7zramLCVrfOqd1kLa3iw7SN56FO/Z13xFxDnAOgKSbImJOm4vUEVwXI1wXI1wXI1wXIyTdNJ7l23GJ6X5gx8L4DnmamZl1kHYEiF8AL5S0s6QNgCOBH7ShHGZmVkfLLzFFxGpJHwCuAKYB34iI20dZ7Jzml2zScF2McF2McF2McF2MGFddKCImqiBmZjaF+JvUZmZWygHCzMxKdXSA6OZXckjaUdJVku6QdLukk/P0LSRdKem3+f/m7S5rq0iaJukWSYvy+M6Sbszt4+L80MOUJ2mmpEsk3SXpTkn7dmu7kPShvH/cJukiSRt2S7uQ9A1JDxe/I1arHSg5K9fJryTt1UgeHRsg/EoOVgOnRMRuwD7A+/P2nwb8JCJeCPwkj3eLk4E7C+P/BHwxInYFlgMntqVUrfcl4L8j4sXAy0l10nXtQtL2wAeBORGxO+mhlyPpnnZxLnBI1bRa7eCNwAvz33zg7EYy6NgAQZe/kiMiHoyIm/PwE6SDwPakOjgvz3YeMK8tBWwxSTsAbwK+nscFvB64JM/SFXUhaTPgtcACgIh4KiJW0KXtgvQk5kaSpgMbAw/SJe0iIq4BHquaXKsdHA58K5IbgJmSth0tj04OEGWv5Ni+TWVpK0mzgD2BG4FtIuLBnPQQsE27ytVi/wqcCjybx7cEVkTE6jzeLe1jZ+AR4Jv5ctvXJc2gC9tFRNwP/AvwB1JgWAkspjvbRUWtdjCm42knBwgDJPUA3wP+NiIeL6ZFekZ5yj+nLOkw4OGIWNzusnSA6cBewNkRsSewiqrLSV3ULjYnnRnvDGwHzOC5l1y61kS0g04OEF3/Sg5J65OCw4URcWme/MdK1zD/f7hd5Wuh/YC3SLqHdKnx9aTr8DPzpQXonvaxFFgaETfm8UtIAaMb28WBwO8j4pGIeBq4lNRWurFdVNRqB2M6nnZygOjqV3Lka+wLgDsj4guFpB8Ax+Xh44Dvt7psrRYRH42IHSJiFqkd/DQijgauAo7Is3VLXTwE3Cep8pbOA4A76MJ2Qbq0tI+kjfP+UqmLrmsXBbXawQ+Av8pPM+0DrCxciqqpo79JLelQ0rXnyis5zmxviVpH0v7AtcCvGbnu/jHSfYgB4AXAvcDbI6L6RtWUJakf+HBEHCZpF1KPYgvgFuCYiPhzG4vXEpL2IN2s3wC4GziBdLLXde1C0qeAd5Ce+rsFeDfp2vqUbxeSLgL6Sa83/yPwSWAhJe0gB9Avky7BPQmcEBGjvum1owOEmZm1TydfYjIzszZygDAzs1IOEGZmVsoBwszMSjlAmJlZqZb/opxZp5D0DOkx4vVJj0l+i/SSt2frLmjWJRwgrJv9KSL2AJC0NfBtYFPS8+TjImlaRDwz3vWYtZMvMZkBEfEw6TXIH8jfNp0m6fOSfpHfn/9eAEnrSfpK/i2GKyX9l6Qjcto9kv5J0s3A2yQdJOl6STdL+m5+rxaS9pZ0taTFkq5o5K2aZu3gAGGWRcTdpG/tb036DYGVEfEK4BXAeyTtDPwlMIv0GyXHAvtWrebRiNgL+DFwOnBgHr8J+Lv8fq1/A46IiL2BbwBd84YAm1x8icms3EHAyyq9A2Az0o+t7A98N9+neEjSVVXLXZz/70MKIv+T3nLABsD1QB+wO3Blnj6N9Kpqs47jAGGW5Xc7PUN6A6aAv4mIK6rmOXSU1ayqzApcGRFHVS3/UuD2iKjueZh1HF9iMgMk9QJfBb6c36N/BfDX+ZIQkl6Uf5jnf4C35nsR25BellbmBmA/Sbvm5WdIehEwBPRK2jdPX1/SS5q5bWZj5R6EdbONJN3KyGOu5wOVV6t/nXSv4eb8JsxHSD/f+D1GXit9H3Az6ZfM1hIRj0g6HrhI0vPy5NMj4jf5stVZ+edDp5PeWHz7xG+e2fj4ba5m60hST0QMS9oS+DmwX/6dBrMpxT0Is3W3SNJM0o3nf3BwsKnKPQgzMyvlm9RmZlbKAcLMzEo5QJiZWSkHCDMzK+UAYWZmpf4/7n/kE4FxEgAAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Creating an erdos-renyi graph or a #binomial graph with 100 nodes and edge-probability distribution of 0.3\n",
+    "G = nx.erdos_renyi_graph(100,0.3,seed=4812)\n",
+    "create_and_plot_graph(G,0.3)\n",
+    "# Creating an erdos-renyi graph with 100 nodes and an edge probability of 0.6\n",
+    "G2=nx.erdos_renyi_graph(100,0.6,seed=4812)\n",
+    "create_and_plot_graph(G2,0.6)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "428135b3",
+   "metadata": {},
+   "source": [
+    "### Inference\n",
+    "The higher the probability parameter, the more the number of edges are generated. Hence, even though the number of nodes remain the same, the edges generated when the probability is 0.6 is more in number. \n",
+    "The expected degrees of the graphs would be $n*p$, where $n$ is the number of nodes and $p$ is the edge-probability. Hence, in the case $p=0.3$, the expected degree of the nodes is $\\approx30$. On performing a similar analysis in the case where $p=0.6$, the expected degree of the nodes is $approx60$. \n",
+    "The clustering of the degrees around the expected probabilities can be observed from the degree centrality distribution as well. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0ea8127",
+   "metadata": {},
+   "source": [
+    "## Barabasi Albert Graph"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "406f8ed4",
+   "metadata": {},
+   "source": [
+    "Barabasi-Albert algorithm generates graphs based on a preferential attachment. New nodes attach to existing nodes that have higher existing connections. It is one of the most popular random graph generator algorithms for scale-free networks.\n",
+    "$G(n,m)$ where $n$ is the number of nodes and $m$ is the number of edges that connect a new node with existing nodes."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "78981787",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Visualizing how the barabasi albert graph grows\n",
+    "gs1 = nx.star_graph(3)\n",
+    "nx.draw(gs1,pos=nx.circular_layout(gs1),with_labels=True)\n",
+    "plt.show()\n",
+    "#Creating a random graph with 8 nodes and 3 edges\n",
+    "Gb1 = nx.barabasi_albert_graph(8,3,seed=7)\n",
+    "nx.draw(Gb1,pos=nx.circular_layout(Gb1),with_labels=True)\n",
+    "plt.show()\n",
+    "# Initial graph when adding an extra node\n",
+    "Gb2 = nx.barabasi_albert_graph(9,3,seed=7,initial_graph=Gb1)\n",
+    "nx.draw(Gb2,pos=nx.circular_layout(Gb2),with_labels=True)\n",
+    "plt.show()\n",
+    "# No intial graph when adding an extra node\n",
+    "gs2 = nx.barabasi_albert_graph(9,3,seed=7)\n",
+    "nx.draw(gs2,pos=nx.circular_layout(gs2),with_labels=True)\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "id": "7c0b00fc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "G3 = nx.barabasi_albert_graph(1000,3,seed=4182)\n",
+    "create_and_plot_graph(G3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "205902e4",
+   "metadata": {},
+   "source": [
+    "### Inference\n",
+    "The degree centrality distribution in graphs generated by Barabasi-Albert algorithm follow the *power-law distribution*. This is expected since the preferential attachment rule ensures that new nodes connect to existing nodes that are highly connected."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "db6454c9",
+   "metadata": {},
+   "source": [
+    "## Comparison between the 2 algorithms\n",
+    "The **Erdos-Renyi** algorithm generates random graphs that ensure that the degree of the nodes can be manipulated by fixed an edge probability. The edge probability dictates the probability of an edge existing between 2 nodes. The degree of the nodes tend to cluster around $n*p$ where $n$ is the number of nodes and $p$ is the edge probability.\n",
+    "     $\\newline$\n",
+    "On the other hand, **Barabasi-Albert** algorithm is a scale-free algorithm whose degree distribution follows power-law. New nodes preferentially attach themselves to existing nodes that show a high degree. Hence, the number of nodes that show a very high degree are few in number."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/2022-round-1/arpitadash/nx_tutorial_script.py b/2022-round-1/arpitadash/nx_tutorial_script.py
new file mode 100644
index 0000000..a3eda76
--- /dev/null
+++ b/2022-round-1/arpitadash/nx_tutorial_script.py
@@ -0,0 +1,29 @@
+import networkx as nx
+import matplotlib.pyplot as plt
+
+#Creating a networkX digraph
+G=nx.DiGraph()
+#Adding nodes of int, str and tuple type
+G.add_node(1)
+G.add_node("string1")
+G.add_node((6,2))
+G.add_node('string2')
+G.add_nodes_from([2,3,5])
+G.add_nodes_from([(4,{'color':'red'})])
+#Adding edges between the nodes
+G.add_edge(4,1)
+G.add_edges_from([(1,2),(1,3),(1,'string1'),(2,3),('string2',1),(1,'string2'),(1,(6,2)),(2,5),((6,2),'string2'),('string2',4)])
+#Calculating shortest path between all nodes in the graph
+p=nx.shortest_path(G)
+print('Printing shortest path')
+#Storing existing nodes in the graph
+G_node_list = G.nodes
+for index,node in enumerate(G_node_list):
+    print('From',node)
+    for index2,node2 in enumerate(G_node_list):
+        if index!=index2 and nx.has_path(G, node, node2):
+            print('To', node2, ':', p[node][node2])
+#Plotting the graph
+nx.draw(G,pos=nx.circular_layout(G),with_labels=True)
+plt.show()
+
diff --git a/2022-round-1/arpitadash/nx_version.txt b/2022-round-1/arpitadash/nx_version.txt
new file mode 100644
index 0000000..860487c
--- /dev/null
+++ b/2022-round-1/arpitadash/nx_version.txt
@@ -0,0 +1 @@
+2.7.1