除邻接表与邻接矩阵外，还有哪些图表示的数据结构？

Great question! It's cool that you stumbled upon the graph representation using source_indices and destination_offsets in the NVIDIA CUDA Toolkit—this is actually a GPU-optimized variant of the Compressed Sparse Row (CSR) format, a go-to for efficient parallel graph processing. If you're hunting for alternatives to the classic adjacency matrix and list, here are some practical, lesser-discussed options:

• Coordinate List (COO)
  The simplest edge-centric format: store two parallel arrays, one for source nodes (src) and one for destination nodes (dst). For example, src = [0, 0, 1] and dst = [1, 2, 0] represents edges 0→1, 0→2, and 1→0. It’s intuitive and great for bulk edge operations (like importing/exporting graph data), but slow for per-node neighbor queries. Many CUDA graph workflows start with COO before converting to CSR for better performance.

• Compressed Sparse Column (CSC)
  The symmetric counterpart to CSR. Instead of organizing edges by source nodes, it groups them by destination nodes using a col_ptr offset array and row_idx index array. This is ideal for tasks that require frequent queries of incoming neighbors (like reverse graph traversals or calculating in-degrees at scale).

• Edge Array with Attributes
  A variation of COO that bundles edge properties (like weights, capacities, or labels) directly with each edge. For example, a struct like:

  struct WeightedEdge {
      int src;
      int dst;
      float weight;
  };
  

  This format shines for weighted graphs or any scenario where edge metadata is critical (e.g., shortest path algorithms, network flow problems).

• Bitmask Representation
  Perfect for small, dense graphs or binary edge relationships (no weights). Each node is represented by a bit vector, where the i-th bit is set to 1 if there’s an edge to node i. This saves memory compared to adjacency matrices and enables fast bitwise operations (like finding common neighbors with a bitwise AND). It’s especially useful for graph algorithms that rely on set operations.

• Dynamic Graph Structures
  For graphs that require frequent edge/node additions or deletions, static formats like CSR become inefficient. Instead, use:

  • Linked-list adjacency lists (each node’s neighbors are stored in a linked list for O(1) insertions/deletions)
  • Hash-table adjacency lists (each node maps to a hash set of neighbors, enabling fast lookups and modifications)
  • Advanced structures like skip lists or radix trees for balanced performance across all operations.

• Layered Graph Formats
  Tailored for directed acyclic graphs (DAGs) or hierarchical graphs (e.g., neural network computation graphs, workflow graphs). Nodes are grouped into layers, and edges are stored as connections between consecutive layers. This format optimizes parallel processing by allowing entire layers to be computed simultaneously, which is why it’s widely used in deep learning frameworks.

The source_indices/destination_offsets format you found in CUDA is just CSR adapted for GPU memory patterns—its linear array structure avoids pointer overhead and aligns with how GPUs efficiently access memory.

内容的提问来源于stack exchange，提问作者Jenil Mewada