Is opencv matrix data guaranteed to be continuous?

You can see in the OpenCV doc for isContinuous:

The method returns true if the matrix elements are stored continuously without gaps at the end of each row. Otherwise, it returns false. Obviously, 1×1 or 1xN matrices are always continuous. Matrices created with Mat::create() are always continuous. But if you extract a part of the matrix using Mat::col(), Mat::diag() , and so on, or constructed a matrix header for externally allocated data, such matrices may no longer have this property.

So, as long as you are creating a new matrix (i.e. you’re calling create), your matrix will be continuous.

create works like:

1. If the current array shape and the type match the new ones, return immediately. Otherwise, de-reference the previous data by calling Mat::release().
2. Initialize the new header.
3. Allocate the new data of total()*elemSize() bytes.
4. Allocate the new, associated with the data, reference counter and set it to 1.

This means that when you (implicitly) call create, the matrix will be continuous (step 3).

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Your questions

If I create a new matrix with imread is the data guaranteed to be continuous

Yes, because imread internally calls create.

I know that creating a new matrix by borrowing data from existing matrix would result in incontinuous data.

Correct, data will be non continuous. To make the new matrix continuous, you can call clone(), which calls create to create the new matrix.

if I create a brand new matrix without borrowing data from existing matrix, will the brand new matrix have incontinuous data?

Yes, the constructor internally calls create.

Matrix constructor is guaranteed to create a matrix with continuous data?

Yes, the constructor internally calls create.

This is a small example to summarize:

#include <opencv2\opencv.hpp>
#include <iostream>
using namespace std;
using namespace cv;

int main()
{
    // Read image
    Mat img = imread("path_to_image");
    cout << "img is continuous? " << img.isContinuous() << endl; 
    // Yes, calls create internally

    // Constructed a matrix header for externally allocated data
    Mat small_mat = img.col(0);
    cout << "small_mat is continuous? " << small_mat.isContinuous() << endl; 
    // No, you're just creating a new header.

    // Matrix (self) expression
    small_mat = small_mat + 2;
    cout << "small_mat is continuous? " << small_mat.isContinuous() << endl; 
    // No, you're not even creating a new header

    // Matrix expression
    Mat expr = small_mat + 2;
    cout << "expr is continuous? " << expr.isContinuous() << endl; 
    // Yes, you're creating a new matrix

    // Clone
    Mat small_mat_cloned = img.col(0).clone();
    cout << "small_mat_cloned is continuous? " << small_mat_cloned.isContinuous() << endl; 
    // Yes, you're creating a new matrix

    // Create
    Mat mat(10, 10, CV_32FC1);
    cout << "mat is continuous? " << mat.isContinuous() << endl; 
    // Yes, you're creating a new matrix

    return 0;
}