Explaining the Syntax

vector<int> adj[5] creates $5$ separate vectors. Each adj[i] holds the neighbors of node $i$.

$1.$ adj[0] is a vector that stores neighbors of node $0$.

$2.$ adj[1] is a vector that stores neighbors of node $1$.

$3.$ And so on for adj[2], adj[3], adj[4]. If Node $1$ connects to nodes $2$ and $3$, then adj[1] = {2, 3}. To add a neighbor, use adj[u].push_back(v). To iterate through all neighbors of node $u$, loop through adj[u]. This two-line pattern is the foundation of every graph algorithm you will write. Learn it now because you will use it hundreds of times.