int main()
{
    char a[7] = "Network";
    return 0;
}

A string literal in C is terminated internally with a nul character. So, the above code should give a compilation error since the actual length of the string literal Network is 8 and it cannot fit in a char[7] array.

However, gcc (even with -Wall) on Ubuntu compiles this code without any error or warning. Why does gcc allow this and not flag it as compilation error?

gcc only gives a warning (still no error!) when the char array size is smaller than the string literal. For example, it warns on:

char a[6] = "Network";

[Related] Visual C++ 2012 gives a compilation error for char a[7]:

1>d:\main.cpp(3): error C2117: 'a' : array bounds overflow
1> d:\main.cpp(3) : see declaration of 'a'