  An abstract network approach is proposed for the description of the dynamics
in reactive processes. The phase space of the variables (concentrations in
reactive systems) is partitioned into a finite number of segments, which
constitute the nodes of the abstract network. Transitions between the nodes are
dictated by the dynamics of the reactive process and provide the links between
the nodes. These are weighted networks, since each link weight reflects the
transition rate between the corresponding states-nodes. With this construction
the network properties mirror the dynamics of the underlying process and one
can investigate the system properties by studying the corresponding abstract
network. As a working example the Lattice Limit Cycle (LLC) model is used. Its
corresponding abstract network is constructed and the transition matrix
elements are computed via Kinetic (Dynamic) Monte Carlo simulations. For this
model it is shown that the degree distribution follows a power law with
exponent -1, while the average clustering coefficient $c(N)$ scales with the
network size (number of nodes) $N$ as $c(N)\sim N^{-\nu}, \nu \simeq 1.46$. The
computed exponents classify the LLC abstract reactive network into the
scale-free networks. This conclusion corroborates earlier investigations
demonstrating the formation of fractal spatial patterns in LLC reactive
dynamics due to stochasticity and to the clustering of homologous species. The
present construction of abstract networks (based on the partition of the phase
space) is generic and can be implemented with appropriate adjustments in many
dynamical systems and in time series analysis.
