Unhandled exception when returning a dynamically allocated struct in C

I haven't found a similar question for the problem I've ran into. I am only guessing the root of the error, but I don't have enough knowledge to debug it. The code is as follows:

main.c

#include <stdio.h>
#include "adjacency.h"

int main()
{
    FILE* textfile;
    textfile = fopen("graf.txt", "r");
    adjacency_matrix Graph;
    create_graph(textfile);
}

adjacency.c

#include "adjacency.h"
#include <stdlib.h>
#include <stdio.h>

adjacency_matrix create_graph(FILE* input)
{
    adjacency_matrix graph; int s_node, f_node;
    fscanf(input, "%d", &graph.vertices);
    int i, j;
    graph.matrix = (int**)malloc((graph.vertices + 1) * sizeof(int*));
    for (i = 0; i <= graph.vertices; i++)
        graph.matrix[i] = (int*)malloc(sizeof(int));
    for (i = 0; i <= graph.vertices; i++)
        for (j = 0; j <= graph.vertices; j++)
            graph.matrix[i][j] = 0;
    for (i = 0; i <= graph.vertices; i++)
        graph.matrix[i][0] = graph.matrix[0][i] = i;
    while (1)
    {
        fscanf(input, "%d %d", &s_node, &f_node);
        if (feof(input))
            break;
        graph.matrix[s_node][f_node] = 1;
    }
    return graph;
}

Everything works (I've tested printing the matrix inside the function, before returning the graph struct), but it stops after returning the adjacency_matrix struct called by my function in the main source file.

Visual Studio says

Unhandled exception at 0x77F4A879 (ntdll.dll) in dijkstra.exe: 0xC0000374: A heap has been corrupted (parameters: 0x77F85910). 

then points me to exe_common.inl, on line 292.

if (!has_cctor)
    _cexit();

I would appreciate some help.

I think you need to allocate more memory for the columns of the matrix:

for (i = 0; i <= graph.vertices; i++)
    graph.matrix[i] = (int*)malloc((graph.vertices + 1) * sizeof(int));