Buggy python submission (verdict: Time Limit Exceeded):
N,M = map(int,input().split())    
    
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]
    
    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())
    
A=[None]*M
B=[None]*M

uf = UnionFind(N)
for i in range(M):
    a,b = map(int,input().split())
    uf.union(a-1,b-1)
for i in range(N):
    c = uf.find(i)
    
root = uf.roots()
print( max(len(uf.members(r)) for r in root) )

Fixed submission:
N,M = map(int,input().split())    
       
AB = [None]*M
for i in range(M):
    a,b = map(int,input().split())
    if a>b:
        a,b=b,a
    AB[i] = (a-1,b-1)

AB=set(AB)

tree=[[] for _ in range(N)]
for a,b in AB:
    tree[a].append(b)
    tree[b].append(a) #aがbの親、とかが保証されてれば不要。

from collections import deque

groups=[]
been=[0]*N
for i in range(N):
    if been[i]==0:
        group=[i]
        been[i]=1
        q = deque([(i,togo) for togo in tree[i]]) 
        while q:
            parent,x = q.popleft()
            if been[x]==1:
                continue
            been[x]=1
            group.append(x)
            for y in tree[x]:
                if y == parent:#親ノードを飛ばし
                    continue
                q.append((x,y))#子ノードを追加
        groups.append(group)

print(max( len(g) for g in groups))

Buggy python submission (verdict: Time Limit Exceeded):
N,M = map(int,input().split())    
    
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]
    
    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())
 

uf = UnionFind(N)
for i in range(M):
    a,b = map(int,input().split())
    uf.union(a-1,b-1)

root = uf.roots()
print( max(len(uf.members(r)) for r in root) )

Fixed submission:
N,M = map(int,input().split())    
       
AB = [None]*M
for i in range(M):
    a,b = map(int,input().split())
    if a>b:
        a,b=b,a
    AB[i] = (a-1,b-1)

AB=set(AB)

tree=[[] for _ in range(N)]
for a,b in AB:
    tree[a].append(b)
    tree[b].append(a) #aがbの親、とかが保証されてれば不要。

from collections import deque

groups=[]
been=[0]*N
for i in range(N):
    if been[i]==0:
        group=[i]
        been[i]=1
        q = deque([(i,togo) for togo in tree[i]]) 
        while q:
            parent,x = q.popleft()
            if been[x]==1:
                continue
            been[x]=1
            group.append(x)
            for y in tree[x]:
                if y == parent:#親ノードを飛ばし
                    continue
                q.append((x,y))#子ノードを追加
        groups.append(group)

print(max( len(g) for g in groups))