segmentation fault at c program when input is large - c

Question

I'm working on a program that checks whether or not a graph given from an input file has some specific criteria (e.g. it's connected etc).
Although yesterday I made it work, I'm trying to tweak it a bit so it runs faster, but that leads me to the well-known segmentation fault error.
What I'm findind really frustrating is that, after tried debugging of my own, I realised that I get the error after allocating the memory I need for the graph and only when the graph gets really big, for example over 500000 nodes and edges. (I'm using a linked list for the graph).
I've been writing in C for some years and I know (or at least I think I do) that "segmentation fault" pops up when the process tries to access memory that is not supposed to, but I can't understand why it's happening in that case.
GDB gave me the below info:
Program received signal SIGSEGV, Segmentation fault.
0x0000555555554b28 in checkConnectivity (hd=<error reading variable: Cannot access memory at address 0x7fffff7feff8>, currentNode=<error reading variable: Cannot access memory at address 0x7fffff7feff0>, pointerToNode=<error reading variable: Cannot access memory at address 0x7fffff7fefe8>) at test.c:140
140 void checkConnectivity(node *hd, node *currentNode, node *pointerToNode[N])
checkConnectivity is a function that, using DFS, tries to check if the graph is connected or not. It has 3 arguments, hd the head pointer of my linked list, currentNode the node I am right now and pointerToNode, an array of pointers for getting to nodes faster (this is the tweak I wrote before about).
As you can tell hd and pointerToNode never change. I also call recursively the function after testing that I've not been yet to currentNode. So why i get this kind of error after calling it over again and again?
Any help/ideas would be much appreciated.
PS: I know that providing some code would be way more enlightening,
but my code is too long to include it in the question.
/edit/
void *safeMalloc(size_t size) {
void *p;
if((p = malloc(size)) == NULL) {
printf("Error 1 at safeMalloc.\nTerminating the program...\n");
exit(0);
}
return p;
}
typedef struct node {
long int id;
long int numOfNeighbors;
int visited;
struct neighbor *nextNeighbor;
struct node *nextNode;
} node;
typedef struct neighbor {
long int id;
struct neighbor *nextNeighbor;
} neighbor;
void checkConnectivity(node *hd, node *currentNode, node *pointerToNode[N]) {
//Mark our current node as visited.
currentNode->visited = 1;
//Find its first unvisited neighbor and call the function recursively.
if (currentNode->nextNeighbor == NULL) {
//No neighbors, return.
return;
} else {
neighbor *currentNeighbor = currentNode->nextNeighbor;
while (1) {
//If we haven't visited this neighbor yet...
if (pointerToNode[currentNeighbor->id - 1]->visited == 0) {
//Visit it.
checkConnectivity(hd, pointerToNode[currentNeighbor->id - 1], pointerToNode);
}
//Find the next neighbor of our node.
if (currentNeighbor->nextNeighbor != NULL) {
currentNeighbor = currentNeighbor->nextNeighbor;
} else {
return;
}
}
}
}
I think that the code above is enough to give you some idea of what I'm trying to do.
Node struct is for every node of my graph and every node points to every one of its neighbors (that's what neighbor struct is for), besides the next (numerically) node of the graph. Note that a link between two nodes struct doesn't mean an edge between them. This whole idea of representing a graph is taken from this article, but the code is mine.
Hope this helps! Thanks for your time.