  The purpose of this paper is to exhibit a quantum network phenomenon - the
anti-core---that goes against the classical network concept of congestion core.
Classical networks idealized as infinite, Gromov hyperbolic spaces with
least-cost path routing (and subject to a technical condition on the Gromov
boundary) have a congestion core, defined as a subnetwork that routing paths
have a high probability of visiting. Here, we consider quantum networks, more
specifically spin chains, define the so-called maximum excitation transfer
probability $p_{\max}(i,j)$ between spin $i$ and spin $j$, and show that the
central spin has among all other spins the lowest probability of being excited
or transmitting its excitation. The anti-core is singled out by analytical
formulas for $p_{\mathrm{max}}(i,j)$, revealing the number theoretic properties
of quantum chains. By engineering the chain, we further show that this
probability can be made vanishingly small.
