This jobs can be done once you are able to find out the middle node of the Link List. Assuming the link list is single link list we can follow the following algo -
1. Take two pointers slow_ptr and fast_ptr.
2. make fast_ptr move two nodes in slow_ptr moves one node in each iteration more than slow *ptr.
3. when fast_ptr reaches to null then slow_ptr will point to middle node and you can delete it.
Void deleteMidddle(Node* head)
Node* slow_ptr = head;
Node* fast_ptr = head;
Node* tmp = head;
while(slow_ptr->next != NULL && fast_ptr->next != NULL)
tmp = slow_ptr;
slow_ptr = slow_ptr->next;
fast_ptr = fast_ptr->next->next;
tmp->next = slow_ptr->next;