Example 4: Sparse Multiple Canonical Correlation Network (SmCCNet) + PageRank Clustering + Visualization
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This example demonstrates a comprehensive workflow that integrates network construction, clustering, and visualization to explore patterns in multi-omics data.

**Workflow Overview:**

1. **Network Construction (SmCCNet):**
   Generates an adjacency matrix from multi-omics data using `SmCCNet`. The resulting matrix represents relationships between features.

2. **PageRank-Based Clustering:**
   Applies the `PageRank` clustering method to identify meaningful sub-networks (clusters) within the constructed network.

3. **Visualization:**
   Visualizes the identified clusters using a static visualization tool (`StaticVisualizer`) to provide insights into the network structure.

**Step-by-Step Guide:**

1. **Setup Input Files:**

   Ensure the following input files are available in the `input/` directory:
   - **Proteins Data (`proteins.csv`)**: Contains protein features.
   - **Metabolites Data (`metabolites.csv`)**: Contains metabolite features.
   - **Phenotype Data (`phenotype_data.csv`)**: Contains phenotype labels.

   Example structure:

   .. code-block:: none

      Proteins.csv:
      protein_feature1,protein_feature2
      0.1,0.3
      0.2,0.4

      Metabolites.csv:
      metabolite_feature1,metabolite_feature2
      0.5,0.7
      0.6,0.8

      Phenotype_data.csv:
      phenotype
      1
      0

2. **Run SmCCNet:**

   Use `SmCCNet` to construct the network:

   .. literalinclude:: ../examples/example_4.py
      :language: python
      :lines: 21-33
      :caption: Running SmCCNet to generate the adjacency matrix.

   This step constructs the adjacency matrix, which encodes relationships between features in the omics data.

3. **Run PageRank Clustering:**

   Apply PageRank-based clustering to identify sub-networks (clusters) from the constructed network:

   .. literalinclude:: ../examples/example_4.py
      :language: python
      :lines: 43-67
      :caption: Running PageRank-based clustering.

   This step identifies clusters using seed nodes you specify.

4. **Visualization:**

   Visualize the identified clusters using a static visualization tool:

   .. literalinclude:: ../examples/example_4.py
      :language: python
      :lines: 77-82
      :caption: Visualizing the identified cluster.

   The visualization provides a graphical view of the network, highlighting clusters of interest. The resulting image is saved in the `visualization_output/` directory.

**Running the Example:**

To execute the complete workflow:

.. literalinclude:: ../examples/example_4.py
   :language: python
   :caption: Complete SmCCNet + PageRank Clustering + Visualization Workflow.

Upon successful execution, the workflow outputs:
- **Adjacency Matrix**: Generated by SmCCNet, saved as a CSV file.
- **Clustering Results**: Saved in the `pagerank_output/` directory.
- **Visualization**: Saved as an image in the `visualization_output/` directory.

**Result Interpretation:**

- **Adjacency Matrix**: Represents relationships between features in the omics data.
- **Clustering Results**: Provides metrics like cluster size, conductance, correlation, composite score, and p-value.
- **Visualization**: Offers a graphical representation of the sub-network, revealing patterns and connections among features.