#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;

#define rep(i,n) for(ll i=0;i<n;++i)
#define all(a) (a).begin(),(a).end()
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T> T div_floor(T a, T b) { return a / b - ((a ^ b) < 0 && a % b); }
template<class T> T div_ceil(T a, T b) { return a / b + ((a ^ b) > 0 && a % b); }
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;

void solve() {
    ll N,M;
    cin>>N>>M;
    vector<vector<ll>> edge(N);
    dsu UF(N);
    ll namori_component=-1;
    rep(i,M){
        ll a,b;
        cin>>a>>b;
        a--;
        b--;
        edge[a].push_back(b);
        edge[b].push_back(a);
        if (!UF.merge(a,b)){
            namori_component=a;
        };
    }
    if (M!=N-1){
        cout<<"No"<<endl;
        return;
    }
    if (UF.size(0)==N){ // 連結の場合
        vector<ll> dist_to_leaf(N,1e9);
        queue<ll> qu;
        rep(i,N){
            if (edge[i].size()==1){
                qu.push(i);
                dist_to_leaf[i]=0;
            }
        }
        while (qu.size()>0){
            ll cp=qu.front();qu.pop();
            for (ll np:edge[cp]){
                if (chmin(dist_to_leaf[np],dist_to_leaf[cp]+1)){
                    qu.push(cp);
                }
            }
        }
        ll mdist=*max_element(all(dist_to_leaf));
        vector<ll> able;
        rep(i,N){
            if (edge[i].size()==2 and dist_to_leaf[i]==mdist){
                able.push_back(i);
            }
        }
        if (able.size()!=2){
            cout<<"No"<<endl;
            return;
        }
        ll a=able[0];
        ll b=able[1];
        edge[a].push_back(b);
        edge[b].push_back(a);
    }
    else{ // 非連結の場合
        vector<ll> dist_namori(N,1e9);
        queue<ll> qu;
        rep(i,N){
            if (UF.same(namori_component,i)){
                if (edge[i].size()>=4){
                    cout<<"No"<<endl;
                    return;
                }
                if (edge[i].size()==3){
                    dist_namori[i]=0;
                    qu.push(i);
                }
            }
        }
        while (qu.size()>0){
            ll cp=qu.front();qu.pop();
            for (ll np:edge[cp]){
                if (chmin(dist_namori[np],dist_namori[cp]+1)){
                    qu.push(np);
                }
            }
        }
        ll min_dist=1e8;
        ll min_v=-1;
        rep(i,N){
            if (edge[i].size()==1){
                if (chmin(dist_namori[i],min_dist)){
                    min_v=i;
                }
            }
        }
        ll a=min_v;
        ll b=-1;
        rep(i,N){
            if (UF.same(namori_component,i))continue;
            if (edge[i].size()==1){
                b=i;
            }
        }
        edge[a].push_back(b);
        edge[b].push_back(a);
        UF.merge(a,b);
    }
    // 岩井星人グラフの判定
    vector<ll> dist_namori(N,1e9);
    queue<ll> qu;
    rep(i,N){
        if (edge[i].size()>=4){
            cout<<"No"<<endl;
            return;
        }
        if (edge[i].size()==3){
            dist_namori[i]=0;
            qu.push(i);
        }
    }
    while (qu.size()>0){
        ll cp=qu.front();qu.pop();
        for (ll np:edge[cp]){
            if (chmin(dist_namori[np],dist_namori[cp]+1)){
                qu.push(np);
            }
        }
    }
    ll c1=0,c2=0,c3=0;
    ll d3=0;
    rep(i,N){
        if (edge[i].size()==1){
            c1++;
        }
        else if (edge[i].size()==2){
            c2++;
        }
        else if (edge[i].size()==3){
            c3++;
        }
        else{
            assert (false);
        }
    }
    ll X=c1;
    if (X!=c3){
        cout<<"No"<<endl;
        return;
    }
    if (N%X!=0){
        cout<<"No"<<endl;
        return;
    }
    ll Y=N/X;
    rep(i,N){
        if (edge[i].size()==1){
            if (dist_namori[i]!=Y-1){
                cout<<"No"<<endl;
                return;
            }
        }
    }
    cout<<"Yes"<<endl;
    return;
}


int main() {
    ll T=1;
    while (T--){
        solve();
    }
    return 0;
}