  An immersion of a graph $H$ into a graph $G$ is a one-to-one mapping $f:V(H)
\to V(G)$ and a collection of edge-disjoint paths in $G$, one for each edge of
$H$, such that the path $P_{uv}$ corresponding to edge $uv$ has endpoints
$f(u)$ and $f(v)$. The immersion is strong if the paths $P_{uv}$ are internally
disjoint from $f(V(H))$. It is proved that for every positive integer $t$,
every simple graph of minimum degree at least $200t$ contains a strong
immersion of the complete graph $K_t$. For dense graphs one can say even more.
If the graph has order $n$ and has $2cn^2$ edges, then there is a strong
immersion of the complete graph on at least $c^2 n$ vertices in $G$ in which
each path $P_{uv}$ is of length 2. As an application of these results, we
resolve a problem raised by Paul Seymour by proving that the line graph of
every simple graph with average degree $d$ has a clique minor of order at least
$cd^{3/2}$, where $c>0$ is an absolute constant.
  For small values of $t$, $1\le t\le 7$, every simple graph of minimum degree
at least $t-1$ contains an immersion of $K_t$ (Lescure and Meyniel, DeVos et
al.). We provide a general class of examples showing that this does not hold
when $t$ is large.
