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ggml separates the definition of a computation from its execution. When you call ggml_add, ggml_mul_mat, or any other operation, no arithmetic is performed — instead, a new tensor node is allocated that records the operation and its inputs. Actual computation runs only when you call a graph compute function. This design means:
  • The same graph can be executed repeatedly (e.g., for each inference batch) without re-allocation overhead.
  • Backends (CPU, CUDA, Metal, …) receive the full graph and can optimize execution order, fuse kernels, and schedule memory.

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The ggml_cgraph structure

A computation graph is represented by ggml_cgraph, which tracks:
  • nodes — tensors that require computation (operation outputs)
  • leafs — tensors with no inputs (parameters, constants)
  • grads — gradient tensors, populated after ggml_build_backward_expand
Create a graph inside a context: 
// Default size (GGML_DEFAULT_GRAPH_SIZE = 2048 nodes), no gradient storage
struct ggml_cgraph * gf = ggml_new_graph(ctx);

// Custom size and optional gradient support
struct ggml_cgraph * gf = ggml_new_graph_custom(ctx, 4096, /*grads=*/true);

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Full workflow

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Step 1 — Initialize a context

// Calculate required buffer size up front
size_t ctx_size = 0;
ctx_size += rows_A * cols_A * ggml_type_size(GGML_TYPE_F32); // tensor a
ctx_size += rows_B * cols_B * ggml_type_size(GGML_TYPE_F32); // tensor b
ctx_size += 2 * ggml_tensor_overhead();  // metadata for each tensor
ctx_size += ggml_graph_overhead();       // graph struct overhead
ctx_size += 1024;                        // some slack

struct ggml_init_params params = {
    /*.mem_size   =*/ ctx_size,
    /*.mem_buffer =*/ NULL,   // let ggml allocate internally
    /*.no_alloc   =*/ false,
};

struct ggml_context * ctx = ggml_init(params);

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Step 2 — Create tensors and define operations

Operations return new tensor nodes but perform no computation: 
// f(x) = a*x^2 + b
struct ggml_tensor * x  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, 1);
struct ggml_tensor * a  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, 1);
struct ggml_tensor * b  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, 1);
struct ggml_tensor * x2 = ggml_mul(ctx, x, x);
struct ggml_tensor * f  = ggml_add(ctx, ggml_mul(ctx, a, x2), b);

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Step 3 — Build the forward graph

ggml_build_forward_expand walks the tensor graph upward from the output node and registers all reachable nodes into gf: 
struct ggml_cgraph * gf = ggml_new_graph(ctx);
ggml_build_forward_expand(gf, f);

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Step 4 — Set input values

ggml_set_f32(x, 2.0f);
ggml_set_f32(a, 3.0f);
ggml_set_f32(b, 4.0f);

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Step 5 — Compute

ggml_graph_compute_with_ctx(ctx, gf, /*n_threads=*/1);

printf("f = %f\n", ggml_get_f32_1d(f, 0));  // 3*4 + 4 = 16.0

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Step 6 — Free

ggml_free(ctx);

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Matrix multiplication example

The following is adapted from examples/simple/simple-ctx.cpp: 
void load_model(simple_model & model, float * a, float * b,
                int rows_A, int cols_A, int rows_B, int cols_B)
{
    size_t ctx_size = 0;
    ctx_size += rows_A * cols_A * ggml_type_size(GGML_TYPE_F32);
    ctx_size += rows_B * cols_B * ggml_type_size(GGML_TYPE_F32);
    ctx_size += 2 * ggml_tensor_overhead();
    ctx_size += ggml_graph_overhead();
    ctx_size += 1024;

    struct ggml_init_params params = {
        /*.mem_size   =*/ ctx_size,
        /*.mem_buffer =*/ NULL,
        /*.no_alloc   =*/ false,
    };

    model.ctx = ggml_init(params);
    model.a   = ggml_new_tensor_2d(model.ctx, GGML_TYPE_F32, cols_A, rows_A);
    model.b   = ggml_new_tensor_2d(model.ctx, GGML_TYPE_F32, cols_B, rows_B);

    memcpy(model.a->data, a, ggml_nbytes(model.a));
    memcpy(model.b->data, b, ggml_nbytes(model.b));
}

struct ggml_cgraph * build_graph(const simple_model & model) {
    struct ggml_cgraph * gf = ggml_new_graph(model.ctx);

    // result = a * b^T
    struct ggml_tensor * result = ggml_mul_mat(model.ctx, model.a, model.b);
    ggml_build_forward_expand(gf, result);
    return gf;
}

struct ggml_tensor * compute(const simple_model & model) {
    struct ggml_cgraph * gf = build_graph(model);
    ggml_graph_compute_with_ctx(model.ctx, gf, /*n_threads=*/1);
    return ggml_graph_node(gf, -1); // last node = output
}

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Marking tensors as inputs and outputs

When using the backend allocator (ggml_gallocr), you should mark tensors explicitly so that the allocator can make better decisions about memory layout: 
// Inputs are allocated at the start of the graph in non-overlapping addresses
ggml_set_input(tensor);

// Output tensors are never freed or overwritten during graph execution
ggml_set_output(tensor);
These correspond to GGML_TENSOR_FLAG_INPUT and GGML_TENSOR_FLAG_OUTPUT in tensor->flags.

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Inspecting the graph

int n = ggml_graph_n_nodes(gf);
for (int i = 0; i < n; i++) {
    struct ggml_tensor * node = ggml_graph_node(gf, i);
    printf("%s: %s\n", node->name, ggml_op_name(node->op));
}

// Dump as Graphviz dot
ggml_graph_dump_dot(gf, NULL, "graph.dot");

// Print summary
ggml_graph_print(gf);
Pass -1 to ggml_graph_node to get the last node, which is typically the final output tensor:
struct ggml_tensor * out = ggml_graph_node(gf, -1);

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Compute functions reference

Convenience wrapper that allocates the work buffer inside the context. Requires that you have reserved enough space in the context for the work buffer.
enum ggml_status ggml_graph_compute_with_ctx(
    struct ggml_context * ctx,
    struct ggml_cgraph  * cgraph,
    int                   n_threads);
Lower-level API that lets you supply your own work buffer.
struct ggml_cplan plan = ggml_graph_plan(cgraph, n_threads, /*threadpool=*/NULL);
if (plan.work_size > 0) {
    plan.work_data = malloc(plan.work_size);
}
ggml_graph_compute(cgraph, &plan);
free(plan.work_data);
When using a hardware backend, dispatch through the backend scheduler:
// From simple-backend.cpp
ggml_backend_sched_reset(model.sched);
ggml_backend_sched_alloc_graph(model.sched, gf);
ggml_backend_tensor_set(model.a, matrix_A, 0, ggml_nbytes(model.a));
ggml_backend_tensor_set(model.b, matrix_B, 0, ggml_nbytes(model.b));
ggml_backend_sched_graph_compute(model.sched, gf);