  Biological systems, particularly the brain, are frequently analyzed as
networks, conveying mechanistic insights into their function and
pathophysiology. This is the first study of a functional network of cardiac
tissue. We use calcium imaging to obtain two functional networks in a
subsidiary but essential pacemaker of the heart, the atrioventricular node
(AVN). The AVN is a small cellular structure with dual functions: a) to delay
the pacemaker signal passing from the sinoatrial node (SAN) to the ventricles,
and b) to serve as a back-up pacemaker should the primary SAN pacemaker fail.
Failure of the AVN can lead to syncope and death. We found that the shortest
path lengths and clustering coefficients of the AVN are remarkably similar to
those of the brain. The network is ``small-world," thus optimized for energy
use vs transmission efficiency. We further study the network properties of AVN
tissue with knock-out of the sodium-calcium exchange transporter. In this case,
the average shortest path-lengths remained nearly unchanged showing network
resilience, while the clustering coefficient was somewhat reduced, similar to
schizophrenia in brain networks. When we removed the global action potential
using principal component analysis (PCA) in wild-type model, the network lost
its ``small-world" characteristics with less information-passing efficiency due
to longer shortest path lengths but more robust signal propagation resulting
from higher clustering. These two wild-type networks (with and without global
action potential) may correspond to fast and slow conduction pathways. Laslty,
a one-parameter non-linear preferential attachment model is a good fit to all
three AVN networks.
