diff --git a/HW03/scripts/demo3a.py b/HW03/scripts/demo3a.py
new file mode 100644
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+++ b/HW03/scripts/demo3a.py
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+#
+# Demo 3a: Non-recursive normalized cuts
+#
+# author: Christos Choutouridis <cchoutou@ece.auth.gr>
+# date:   06/07/2025
+#
+try:
+    # Testing requirements
+    from scipy.io import loadmat
+    import matplotlib.pyplot as plt
+    import numpy as np
+
+    # Project imports
+    from normalized_cuts import n_cuts
+    from spectral_clustering import spectral_clustering
+    from image_to_graph import image_to_graph
+except ImportError as e:
+    print("Missing package:", e)
+    print("Run: pip install -r requirements.txt")
+    exit(1)
+
+
+
+
+def plot_segmentation(image, labels, k, title, fname):
+    M, N, _ = image.shape
+    segmented = labels.reshape(M, N)
+    plt.imshow(segmented, cmap='tab10', vmin=0, vmax=k-1)
+    plt.title(title)
+    plt.axis('off')
+    plt.tight_layout()
+    plt.savefig(fname)
+    print(f"Saved: {fname}")
+    plt.close()
+
+
+def run_demo3a():
+    data = loadmat("dip_hw_3.mat")
+
+    for name in ["d2a", "d2b"]:
+        img = data[name]
+        print(f"\n=== Image {name} ===")
+
+        affinity = image_to_graph(img)
+
+        for k in [2, 3, 4]:
+            print(f"  k = {k}")
+
+            labels_nc = n_cuts(affinity, k=k)
+            labels_sc = spectral_clustering(affinity, k=k, normalized=False)
+            labels_sc_nrm = spectral_clustering(affinity, k=k, normalized=True)
+
+            plot_segmentation(img, labels_nc, k, f"{name} - n_cuts (k={k})", f"plots/demo3a_{name}_ncuts_k{k}.png")
+            plot_segmentation(img, labels_sc, k, f"{name} - spectral (k={k})", f"plots/demo3a_{name}_spectral_k{k}.png")
+            plot_segmentation(img, labels_sc_nrm, k, f"{name} - spectral-Lnorm (k={k})", f"plots/demo3a_{name}_spectral_k{k}_norm.png")
+
+
+if __name__ == '__main__':
+    run_demo3a()
diff --git a/HW03/scripts/demo3b.py b/HW03/scripts/demo3b.py
new file mode 100644
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+++ b/HW03/scripts/demo3b.py
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+#
+# Demo 3b: One-step recursive normalized cuts with Ncut metric
+#
+# author: Christos Choutouridis <cchoutou@ece.auth.gr>
+# date:   06/07/2025
+#
+try:
+    from scipy.io import loadmat
+    import matplotlib.pyplot as plt
+    import numpy as np
+    #Project requirements
+    from image_to_graph import image_to_graph
+    from normalized_cuts import n_cuts, calculate_n_cut_value
+except ImportError as e:
+    print("Missing package:", e)
+    print("Run: pip install -r requirements.txt")
+    exit(1)
+
+
+def plot_split(image, labels, title, fname):
+    M, N, _ = image.shape
+    segmented = labels.reshape(M, N)
+    plt.imshow(segmented, cmap='tab10', vmin=0, vmax=1)
+    plt.title(title)
+    plt.axis('off')
+    plt.tight_layout()
+    plt.savefig(fname)
+    print(f"Saved: {fname}")
+    plt.close()
+
+
+def run_demo3b():
+    data = loadmat("dip_hw_3.mat")
+
+    for name in ["d2a", "d2b"]:
+        img = data[name]
+        print(f"\n=== Image {name} ===")
+
+        affinity = image_to_graph(img)
+
+        labels = n_cuts(affinity, k=2)
+        ncut_val = calculate_n_cut_value(affinity, labels)
+
+        print(f"  Ncut value: {ncut_val:.4f}")
+        plot_split(img, labels, f"{name} - one step n_cuts (Ncut={ncut_val:.4f})", f"plots/demo3b_{name}_ncut.png")
+
+
+if __name__ == '__main__':
+    run_demo3b()
diff --git a/HW03/scripts/demo3c.py b/HW03/scripts/demo3c.py
new file mode 100644
index 0000000..3a5c715
--- /dev/null
+++ b/HW03/scripts/demo3c.py
@@ -0,0 +1,57 @@
+#
+# Demo 3c: Recursive normalized cuts (full version)
+#
+# author: Christos Choutouridis <cchoutou@ece.auth.gr>
+# date:   06/07/2025
+#
+
+try:
+    from scipy.io import loadmat
+    import matplotlib.pyplot as plt
+    import numpy as np
+    #Project requirements
+    from image_to_graph import image_to_graph
+    from normalized_cuts import n_cuts_recursive
+except ImportError as e:
+    print("Missing package:", e)
+    print("Run: pip install -r requirements.txt")
+    exit(1)
+
+def plot_recursive_clusters(image, labels, title, fname):
+    M, N, _ = image.shape
+    segmented = labels.reshape(M, N)
+    plt.imshow(segmented, cmap='tab20')  # tab20 supports up to 20 unique colors
+    plt.title(title)
+    plt.axis('off')
+    plt.tight_layout()
+    plt.savefig(fname)
+    print(f"Saved: {fname}")
+    plt.close()
+
+
+def run_demo3c(T1: float, T2: float):
+    data = loadmat("dip_hw_3.mat")
+
+    for name in ["d2a", "d2b"]:
+        img = data[name]
+        print(f"\n=== Recursive n_cuts on {name} ===")
+
+        affinity = image_to_graph(img)
+        labels = n_cuts_recursive(affinity, T1=T1, T2=T2)
+
+        num_clusters = len(np.unique(labels))
+        print(f"  Clusters found: {num_clusters}")
+        print(f"  Labels: {np.unique(labels)}")
+
+        plot_recursive_clusters(
+            img,
+            labels,
+            title=f"{name} - recursive n_cuts (T1={T1}, T2={T2})",
+            fname=f"plots/demo3c_{name}_recursive_T1-{T1}_T2-{T2}.png"
+        )
+
+
+if __name__ == '__main__':
+    run_demo3c(5, 0.2)
+    run_demo3c(5, 0.95)
+    run_demo3c(5, 0.975)
diff --git a/HW03/scripts/normalized_cuts.py b/HW03/scripts/normalized_cuts.py
new file mode 100644
index 0000000..19ecdca
--- /dev/null
+++ b/HW03/scripts/normalized_cuts.py
@@ -0,0 +1,209 @@
+#
+# Normalized Cuts
+#
+# author: Christos Choutouridis <cchoutou@ece.auth.gr>
+# date:   05/07/2025
+#
+
+try:
+    import numpy as np
+    from numpy.typing import NDArray
+    from sklearn.cluster import KMeans
+    from scipy.sparse.linalg import eigs
+
+    # Testing requirements
+    from scipy.io import loadmat
+    from image_to_graph import image_to_graph
+    import matplotlib.pyplot
+except ImportError as e:
+    print("Missing package:", e)
+    exit(1)
+
+
+def n_cuts(
+    affinity_mat: NDArray[np.floating],
+    k: int
+) -> NDArray[np.int32]:
+    """
+    Non-recursive normalized cuts implementation using spectral embedding.
+
+    Parameters:
+    -----------
+    affinity_mat : np.ndarray of shape (n, n), dtype=float
+        Symmetric affinity matrix representing the graph.
+    k : int
+        Number of clusters.
+
+    Returns:
+    --------
+    cluster_idx : np.ndarray of shape (n,), dtype=int
+        Cluster label for each node.
+    """
+    # Degree matrix
+    D = np.diag(affinity_mat.sum(axis=1))
+
+    # Unnormalized Laplacian
+    L = D - affinity_mat
+
+    # Solve the generalized eigenvalue problem: Lx = λDx
+    eigvals, eigvecs = eigs(A=L, M=D, k=k, which='SR')  # SR = Smallest Real part
+
+    # Each row of U is a node's representation in spectral space
+    # Convert complex -> real (imaginary parts should be negligible)
+    U = np.real(eigvecs)
+
+    # Each row is a vector to be clustered
+    # random_state parameter to 1, to ensure reproducibility across experiments.
+    kmeans = KMeans(n_clusters=k, random_state=1)
+    kmeans.fit(U)
+
+    return kmeans.labels_.astype(np.int32)
+
+
+def calculate_n_cut_value(
+    affinity_mat: NDArray[np.floating],
+    cluster_idx: NDArray[np.int32]
+) -> float:
+    """
+    Calculates the Ncut(A, B) metric for a binary clustering.
+
+    Parameters:
+    -----------
+    affinity_mat : np.ndarray of shape (n, n)
+        Symmetric affinity matrix.
+    cluster_idx : np.ndarray of shape (n,)
+        Cluster labels with values in {0, 1}.
+
+    Returns:
+    --------
+    n_cut_value : float
+        The value of the Ncut metric.
+    """
+    A = np.where(cluster_idx == 0)[0]
+    B = np.where(cluster_idx == 1)[0]
+
+    assoc_AA = np.sum(affinity_mat[np.ix_(A, A)])
+    assoc_BB = np.sum(affinity_mat[np.ix_(B, B)])
+    assoc_AV = np.sum(affinity_mat[A, :])
+    assoc_BV = np.sum(affinity_mat[B, :])
+
+    nassoc_AB = (assoc_AA / assoc_AV) + (assoc_BB / assoc_BV)
+    ncut = 2 - nassoc_AB
+
+    return ncut
+
+
+def n_cuts_recursive(
+    affinity_mat: NDArray[np.floating],
+    T1: int,
+    T2: float
+) -> NDArray[np.int32]:
+    """
+    Recursive normalized cuts clustering.
+
+    Parameters:
+    -----------
+    affinity_mat : np.ndarray of shape (n, n)
+        Symmetric affinity matrix.
+    T1 : int
+        Minimum size for splitting a group.
+    T2 : float
+        Maximum acceptable Ncut value to allow further splitting.
+
+    Returns:
+    --------
+    cluster_idx : np.ndarray of shape (n,), dtype=int
+        Final cluster labels after recursive partitioning.
+    """
+
+    n = affinity_mat.shape[0]
+    cluster_idx = np.zeros(n, dtype=np.int32)
+    next_label = [1]  # Mutable counter to assign new cluster labels
+
+    def recursive_partition(indices: NDArray[np.int32], current_label: int):
+        if len(indices) <= T1:
+            cluster_idx[indices] = current_label
+            return
+
+        sub_affinity = affinity_mat[np.ix_(indices, indices)]
+        labels = n_cuts(sub_affinity, k=2)
+
+        ncut_value = calculate_n_cut_value(sub_affinity, labels)
+        A = indices[labels == 0]
+        B = indices[labels == 1]
+
+        if len(A) <= T1 or len(B) <= T1 or ncut_value > T2:
+            cluster_idx[indices] = current_label
+            return
+
+        # Assign recursively new labels
+        recursive_partition(A, current_label)
+        recursive_partition(B, next_label[0])
+        next_label[0] += 1
+
+    # Start with all indices
+    recursive_partition(np.arange(n), 0)
+    return cluster_idx
+
+
+
+def _test_n_cuts(k: int, plot: bool = False):
+    data = loadmat("dip_hw_3.mat")
+    img = data["d2a"]
+    M, N, _ = img.shape
+
+    print("Running non-recursive n_cuts on d2a...")
+
+    A = image_to_graph(img)
+    labels = n_cuts(A, k=k)
+
+    print("Unique cluster labels:", np.unique(labels))
+
+    # Visualize
+    if plot:
+        clustered = labels.reshape(M, N)
+        matplotlib.use("TkAgg")
+        matplotlib.pyplot.imshow(clustered, cmap='tab10', vmin=0, vmax=2)
+        matplotlib.pyplot.title("n_cuts clustering (k={k}) on d2a")
+        matplotlib.pyplot.axis('off')
+        matplotlib.pyplot.tight_layout()
+        matplotlib.pyplot.show()
+        #matplotlib.pyplot.savefig("ncuts_d2a_k3.png")
+        #print("Saved result to: ncuts_d2a_k3.png")
+
+
+def _test_n_cuts_req(plot: bool = False):
+    data = loadmat("dip_hw_3.mat")
+    img = data["d2b"]
+    M, N, _ = img.shape
+
+    print("Running recursive n_cuts on d2b...")
+
+    affinity = image_to_graph(img)
+
+    # Thresholds from the demo instructions
+    T1 = 5
+    T2 = 0.95
+
+    labels = n_cuts_recursive(affinity, T1=T1, T2=T2)
+
+    print("Number of unique clusters:", len(np.unique(labels)))
+    print("Labels:", np.unique(labels))
+
+    if plot:
+        segmented = labels.reshape(M, N)
+        matplotlib.pyplot.imshow(segmented, cmap='tab20')
+        matplotlib.pyplot.title(f"Recursive n_cuts on d2b (T1={T1}, T2={T2})")
+        matplotlib.pyplot.axis('off')
+        matplotlib.pyplot.tight_layout()
+        matplotlib.pyplot.show()
+        #matplotlib.pyplot.savefig("ncuts_recursive_d2b.png")
+        #print("Saved result to: ncuts_recursive_d2b.png")
+
+if __name__ == '__main__':
+    for k in [2, 3, 4]:
+        _test_n_cuts(k, False)
+
+    _test_n_cuts_req(False)
+
+
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