import random

class GraphEmbedding:
    """
    A placeholder for graph embedding techniques like Node2Vec or DeepWalk.
    Graph embedding aims to represent nodes (or entire graphs) as low-dimensional vectors,
    capturing the graph's structure.

    This implementation will demonstrate a very simple random embedding as a placeholder.
    """
    def __init__(self, graph):
        """
        Initializes the GraphEmbedding object.

        Args:
            graph (dict): An adjacency list representation of the graph.
        """
        self.graph = graph
        self.vertices = list(graph.keys())

    def random_embedding(self, dimensions=128):
        """
        Generates a simple random embedding for each node.
        In a real scenario, this would be replaced by a sophisticated algorithm.

        Args:
            dimensions (int): The dimensionality of the embedding vectors.

        Returns:
            dict: A dictionary mapping each vertex to a random vector.
        """
        embedding = {}
        for vertex in self.vertices:
            embedding[vertex] = [random.uniform(-1, 1) for _ in range(dimensions)]
        return embedding

    def explain_concept(self):
        """
        Provides a brief explanation of graph embedding.
        """
        return (
            "Graph embedding represents graph components (nodes, edges, subgraphs) as vectors "
            "in a low-dimensional space. The goal is to preserve the relationships and "
            "structure of the graph in the vector space. For example, nodes that are close "
            "in the graph should have similar vectors.\n\n"
            "Popular methods include:\n"
            "- DeepWalk: Uses random walks to learn node representations.\n"
            "- Node2Vec: An extension of DeepWalk with more flexible random walks.\n"
            "- Graph Convolutional Networks (GCNs): Use neural networks to learn embeddings by "
            "aggregating information from node neighborhoods."
        )
