#include <bits/stdc++.h>
using namespace std;
constexpr long long mod = 1000000007;
const long long INF = mod * mod;
const double eps = 1e-12;
const double pi = acosl(-1.0);
long long mod_pow(long long x, long long n, long long m = mod) {
  if (n < 0) {
    long long res = mod_pow(x, -n, m);
    return mod_pow(res, m - 2, m);
  }
  if (abs(x) >= m) x %= m;
  if (x < 0) x += m;
  long long res = 1;
  while (n) {
    if (n & 1) res = res * x % m;
    x = x * x % m;
    n >>= 1;
  }
  return res;
}
struct modint {
  long long n;
  modint() : n(0) { ; }
  modint(long long m) : n(m) {
    if (n >= mod)
      n %= mod;
    else if (n < 0)
      n = (n % mod + mod) % mod;
  }
  operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) {
  a.n += b.n;
  if (a.n >= mod) a.n -= mod;
  return a;
}
modint operator-=(modint& a, modint b) {
  a.n -= b.n;
  if (a.n < 0) a.n += mod;
  return a;
}
modint operator*=(modint& a, modint b) {
  a.n = ((long long)a.n * b.n) % mod;
  return a;
}
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, long long n) {
  if (n == 0) return modint(1);
  modint res = (a * a) ^ (n / 2);
  if (n % 2) res = res * a;
  return res;
}
long long inv(long long a, long long p) {
  return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) {
  a = a / b;
  return a;
}
const int max_n = 1 << 16;
modint fact[max_n], factinv[max_n];
void init_f() {
  fact[0] = modint(1);
  for (int i = 0; i < max_n - 1; i++) {
    fact[i + 1] = fact[i] * modint(i + 1);
  }
  factinv[max_n - 1] = modint(1) / fact[max_n - 1];
  for (int i = max_n - 2; i >= 0; i--) {
    factinv[i] = factinv[i + 1] * modint(i + 1);
  }
}
modint comb(int a, int b) {
  if (a < 0 || b < 0 || a < b) return 0;
  return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
  if (a < 0 || b < 0 || a < b) return 0;
  return fact[a] * factinv[a - b];
}
int dist[400][400];
double ma[400][400];
double score[400];
double rg[401];
void solve() {
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) {
      if (i != j) dist[i][j] = mod;
    }
  vector<vector<int>> G(n);
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    dist[a][b] = dist[b][a] = 1;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  for (int i = 1; i <= n; i++) rg[i] = 1 / (double)i;
  for (int k = 0; k < n; k++)
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++) {
        dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
      }
  double ans = 0;
  for (int i = 0; i < n; i++) {
    vector<vector<int>> ids(n);
    for (int j = 0; j < n; j++) {
      ids[dist[i][j]].push_back(j);
    }
    double p = rg[n];
    vector<double> sum(n);
    vector<bool> used(n);
    for (int d = 1; d < n; d++) {
      if (ids[d].empty()) continue;
      fill((sum).begin(), (sum).end(), 0);
      fill((used).begin(), (used).end(), false);
      vector<int> sid;
      for (int id : ids[d]) {
        for (int to : G[id]) {
          used[to] = true;
          sum[to] += rg[n] * rg[G[id].size()];
        }
      }
      for (int j = 0; j < n; j++)
        if (used[j]) {
          for (int k = 0; k < n; k++) {
            int d = dist[j][k];
            if (ma[k][d] < sum[j]) {
              score[k] += sum[j] - ma[k][d];
              ma[k][d] = sum[j];
            }
          }
        }
      double m = rg[n];
      for (int j = 0; j < n; j++) {
        m = max(m, score[j]);
      }
      p += m;
      for (int j = 0; j < n; j++)
        if (used[j]) {
          for (int k = 0; k < n; k++) {
            int d = dist[j][k];
            ma[k][d] = 0;
            score[k] = 0;
          }
        }
    }
    ans = max(ans, p);
  }
  cout << ans << "\n";
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(10);
  solve();
  return 0;
}
