Solutions networkx

Exercise 1

Task 1: Build the graph shown above in networkx using the functions to add graphs. The weight of each edge should correspond to the sum of the node labels it connects.

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import networkx as nx

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G = nx.Graph()

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edges = [
    (0, 1, dict(weight=1)),
    (0, 2, dict(weight=2)),
    (0, 3, dict(weight=3)),
    (0, 4, dict(weight=4)),
    (1, 2, dict(weight=3)),
    (1, 4, dict(weight=5)),
    (2, 3, dict(weight=5)),
    (3, 4, dict(weight=7)),
]

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G.add_edges_from(edges)

Task 2: Draw the finished graph with matplotlib.

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nx.draw(G, with_labels=True)

Exercise 2

Reconsider the example of the European transmission network graph. Use the following code in a fresh notebook to get started:

url = "https://tubcloud.tu-berlin.de/s/FmFrJkiWpg2QcQA/download/edges.csv"
edges = pd.read_csv(url, index_col=0)

G = nx.from_pandas_edgelist(edges, "bus0", "bus1", edge_attr=["x_pu", "s_nom"])

subgraphs = []
for c in nx.connected_components(G):
    subgraphs.append(G.subgraph(c).copy())

Choose one of the subgraphs (each representing a synchronous zone) and perform the following analyses:

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import pandas as pd
import networkx as nx

url = "https://tubcloud.tu-berlin.de/s/FmFrJkiWpg2QcQA/download/edges.csv"
edges = pd.read_csv(url, index_col=0)

G = nx.from_pandas_edgelist(edges, "bus0", "bus1", edge_attr=["x_pu", "s_nom"])

subgraphs = []
for c in nx.connected_components(G):
    subgraphs.append(G.subgraph(c).copy())

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G = subgraphs[3]  # vary the subgraph here

Task 1: Determine the number of transmission lines and buses.

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len(G.edges)

408

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len(G.nodes)

286

Task 2: Check whether the network is planar.

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nx.is_planar(G)

False

Task 3: Calculate the average number of transmission lines connecting to a bus.

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pd.Series({k: v for k, v in G.degree}).mean()

np.float64(2.8531468531468533)

Task 4: Determine the number of cycles forming the cycle basis.

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len(nx.cycle_basis(G))

123

Task 5: Create a histogram of the length of the cycles (i.e. number of edges per cycle) in the cycle basis.

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cycle_length = pd.Series([len(c) for c in nx.cycle_basis(G)])

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cycle_length.plot.hist(bins=100);

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# alternative
pd.Series([len(c) for c in nx.cycle_basis(G)]).value_counts().sort_index().plot();

Task 6: Calculate the average length of the cycles in the cycle basis.

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cycle_length.describe()

count    123.000000
mean       8.918699
std        8.933813
min        3.000000
25%        3.000000
50%        5.000000
75%       11.000000
max       58.000000
dtype: float64

Task 7: Obtain the directed adjacency matrix.

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nx.adjacency_matrix(G).todense()

array([[0, 0, 0, ..., 0, 0, 0],
       [0, 0, 0, ..., 0, 0, 0],
       [0, 0, 0, ..., 0, 0, 0],
       ...,
       [0, 0, 0, ..., 0, 0, 0],
       [0, 0, 0, ..., 0, 0, 0],
       [0, 0, 0, ..., 0, 0, 0]], shape=(286, 286))

Task 8: Obtain the directed incidence matrix.

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K = nx.incidence_matrix(G).todense()
K

array([[1., 1., 0., ..., 0., 0., 0.],
       [0., 0., 1., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       ...,
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.]], shape=(286, 408))