TheAlgorithms/Python · error · ValueError

Node {node_index} should have a list of neighbors.

Error message

Node {node_index} should have a list of neighbors.

What it means

Raised by validate_adjacency_list in graphs/lanczos_eigenvectors.py when the outer object is a list but the element at position node_index is not itself a list of neighbors. Each node must contribute a list (possibly empty) of neighbor indices; a non-list element (int, None, tuple, string) is rejected with ValueError naming the offending index.

Source

Thrown at graphs/lanczos_eigenvectors.py:57

        ValueError: If the graph is not a list of lists, or if any node has
                    invalid neighbors (e.g., out-of-range or non-integer values).

    >>> validate_adjacency_list([[1, 2], [0], [0, 1]])
    >>> validate_adjacency_list([[]])  # No neighbors, valid case
    >>> validate_adjacency_list([[1], [2], [-1]])  # Invalid neighbor
    Traceback (most recent call last):
        ...
    ValueError: Invalid neighbor -1 in node 2 adjacency list.
    """
    if not isinstance(graph, list):
        raise ValueError("Graph should be a list of lists.")

    for node_index, neighbors in enumerate(graph):
        if not isinstance(neighbors, list):
            no_neighbors_message: str = (
                f"Node {node_index} should have a list of neighbors."
            )
            raise ValueError(no_neighbors_message)
        for neighbor_index in neighbors:
            if (
                not isinstance(neighbor_index, int)
                or neighbor_index < 0
                or neighbor_index >= len(graph)
            ):
                invalid_neighbor_message: str = (
                    f"Invalid neighbor {neighbor_index} in node {node_index} "
                    f"adjacency list."
                )
                raise ValueError(invalid_neighbor_message)


def lanczos_iteration(
    graph: list[list[int | None]], num_eigenvectors: int
) -> tuple[np.ndarray, np.ndarray]:
    """Constructs the tridiagonal matrix and orthonormal basis vectors using the
    Lanczos method.

View on GitHub (pinned to f5988cc097)

Solutions

1. Wrap each node's neighbors in a list: `graph = [n if isinstance(n, list) else [n] for n in graph]` only when semantically correct — better, fix construction to always emit lists.
2. Normalize None rows to empty lists: `graph = [row if row is not None else [] for row in graph]`.
3. Validate shape before calling: assert all(isinstance(row, list) for row in graph).

Example fix

# before
graph = [1, 2, 0]  # flat, raises at node 0

# after
graph = [[1, 2], [0], [0]]  # per-node neighbor lists

graph = [row if isinstance(row, list) else [] for row in graph]

def rows_are_lists(graph) -> bool:
    return isinstance(graph, list) and all(isinstance(row, list) for row in graph)

When it happens

Trigger: Passing a flat list of neighbor indices instead of nested lists (e.g. [1, 2, 0]); a row set to None or a tuple; ragged data where one node's entry is a bare int; mixing a numpy row into an otherwise-Python list.

Common situations: Building the adjacency structure node-by-node and forgetting to wrap single neighbors in a list; JSON data where empty neighbor entries deserialize as null; converting only part of a numpy matrix to lists.

Related errors

• Graph should be a list of lists.
• Incorrect input: {vertex} does not exist in this graph.
• Incorrect input: The edge does NOT exist between {source_ver
• Incorrect input: Either {source_vertex} or {destination_vert
• Invalid neighbor {neighbor_index} in node {node_index} adjac

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/f391f7decbe3d66c. Report an issue: GitHub.