# Graph Basicstrue

This section describes the basic concepts you need to know when constructing a graph.

## Framework Bridgestrue

Frontends (or users who require the flexibility of constructing Ops directly) can utilize a set of graph construction functions to construct graphs.

A framework bridge constructs a function which is compiled/optimized by a sequence of graph transformations that replace subgraphs of the computation with more optimal subgraphs. Throughout this process, ops represent tensor operations.

## Tensorstrue

Tensors are maps from coordinates to scalar values, all of the same type, called the element type of the tensor. Coordinates are tuples of non-negative integers; all the coordinates for a tensor have the same length, called the rank of the tensor. We often use $$n$$-tensor for tensors with rank $$n$$.

The shape of a tensor is a tuple of non-negative integers that represents an exclusive upper bound for coordinate values. A tensor has an element for every coordinate less than the shape, so the size of the tensor is the product of the values in the shape.

An $$n$$-dimensional array is the usual implementation for a tensor, and the two terms are often used interchangeably, but a tensor could just as easily be represented by a function that returns 0 for every coordinate or a function that adds the elements of two other tensors at the same coordinate and returns that sum.

## Opstrue

A computation graph is a composition of tensor computations, called ops, which are nodes in the graph. In the graph, every op input must be associated with an op output, and every op output must have a fixed element type and shape to correspond with the tensors used in the computation. Every op has zero or more inputs and zero or more outputs. The outputs represent tensors that will be provided during execution. Ops may also have additional attributes that do not change during execution.

Every op is a Node, but not all nodes are ops. This is because pattern graphs are another kind of graph that includes ops combined with nodes that describe how to match subgraphs during graph optimization.

Constructed ops have element types and shapes for each of their outputs, which are determined during op construction from the element types and shapes associated with the inputs, as well as additional attributes of the ops. For example, tensor addition is defined for two tensors of the same shape and size and results in a tensor with the same element type and shape:

$(A+B)_I = A_I + B_I$

Here, $$X_I$$ means the value of a coordinate $$I$$ for the tensor $$X$$. So the value of sum of two tensors is a tensor whose value at a coordinate is the sum of the elements are that coordinate for the two inputs. Unlike many frameowrks, it says nothing about storage or arrays.

An Add op is used to represent an elementwise tensor sum. To construct an Add op, each of the two inputs of the Add must be assigned some output of some already-created op. All outputs of constructed ops have element types and shapes, so when the Add is constructed, it verifies that the two input tensors have the same element type and shape and then sets its output to have the same element type and shape.

Since all nodes supplying outputs for inputs to a new node must exist before the new node can be created, it is impossible to construct a cyclic graph. Furthermore, type-checking is performed as the ops are constructed.

## Functionstrue

Ops are grouped together in a Function, which describes a computation that can be invoked on tensor arguments to compute tensor results. When called by a bridge, the bridge provides tensors in the form of row-major arrays for each argument and each computed result. The same array can be used for more than one argument, but each result must use a distinct array, and argument arrays cannot be used as result arrays.

Function definition begins with creating one or more Parameter ops, which represent the tensors that will be supplied as arguments to the function. Parameters have no inputs and attributes for the element type and shape of the tensor that will be provided as an argument. The unique output of the Parameter will have the provided element type and shape.

A Function has Parameters, a vector of Parameter ops, where no Parameter op may appear more than once in the vector. A Parameter op has no inputs and attributes for its shape and element type; arrays passed to the function must have the same shape and element type as the corresponding parameter. The Function also has Nodes, a vector of ops that are the results being computed.

During execution, the output of the nth Parameter op will be the tensor corresponding to the array provided as the nth argument, and the outputs of all result ops will be written into the result arrays in row-major order.

## An Exampletrue

#include <memory>
#include <ngraph.hpp>

using ngraph;

// f(a, b, c) = (a + b) * c
void make_function()
{

// First construct the graph
Shape shape{32, 32};
auto a = std::make_shared<op::Parameter>(element::f32, shape);
auto b = std::make_shared<op::Parameter>(element::f32, shape);
auto c = std::make_shared<op::Parameter>(element::f32, shape);