Studying complex tourism systems:
a novel approach based on networks derived from a time series
Rodolfo Baggio
Master in Economics and Tourism and Dondena Centre for Research on Social Dynamics
Bocconi University, Milan, Italy
A tourism destination (TD) is a complex collection of diverse components of interrelated economic,
social and environmental phenomena, all deeply connected among themselves. A TD has been
recognized to be a variable and dynamic system, in which triggering events, both internal or
external, natural or human, can challenge existing structures, normal operations or even the very
existence of the organization and can dislodge the system from an equilibrium state towards new
evolutionary paths. All this with a very little predictability, which makes difficult the governance of
the system and the design of strategies aiming at improving the overall effectiveness and efficiency
of the whole and of its components (Farrell & Twining-Ward, 2004; Russell, 2006).
Analyzing the interaction between its components and the temporal evolution of the system are two
common ways to expose and characterize its internal functioning. In the last years a gradually
growing strand of literature has researched tourism systems, and especially tourism destinations,
from a complex systems science perspective (Baggio et al., 2010a).
The application of different complexity science methods, well known in physics, mathematics
sociology and economics, but not widely used in the tourism literature, has provided already a good
array of insights into the structure and the dynamic behavior of a tourism destination. The general
complexity characteristics have been explored by using non-linear time series analysis techniques
and by applying complex network analysis methods (Baggio, 2008; Baggio & Sainaghi, 2011;
Baggio et al., 2010b).
In the last years, various conceptual approaches have been used for studying the characteristic
features of dynamical systems based on observational time series (Kantz & Schreiber, 1997; Sprott,
2003). Popular methods employed in a variety of applications include: Lyapunov exponents, fractal
dimensions, symbolic discretization, and measures of complexity such as entropies or quantities
derived from them. All these techniques have in common that they measure certain dynamically
invariant properties of the system under study based on temporally discretized realizations of
system’s evolutionary trajectories.
However, their application requires employing sophisticated techniques that rely, in many cases, on
a good and deep experience and knowledge of the researchers. Moreover, all these methods require,
for their best working, amounts of data that are not very common in the tourism field. Nonetheless,
some of these techniques have been applied to the study of a TD, but, despite the existence of
reasonably “usable” software tools, their usage and the interpretation of the results rests a task
which can be difficult for many, especially practitioners (Baggio & Sainaghi, 2011).
The network science approach has uncovered important outcomes concerning TDs’ structures, the
functioning of collaborative and cooperative groups, the diffusion of information, knowledge and
policy messages across the system or the relationships between the physical and the virtual
components of a destination. Additionally, the network approach has been extended to implement
simulation models with which different scenarios can be obtained in order to explore the possible
effects of different managerial or governance activities. This provides people interested in the life of
a tourism destination with powerful tools to inform their policy or management actions. The
network perspective can therefore offer a number of useful outcomes for tourism studies, but has
also shown some limitations mainly due to the difficulty of collecting the data needed to perform a
full analysis (Baggio et al., 2010b, 2011).
Recently, however, new methods have been proposed that allow to derive general characteristics of
a complex system by using a time series of observations and transforming it into a network.
The idea is that we can consider a time series just as a set of numeric values and play a simple game
of transforming it into a different mathematical object. Then we can check what properties of the
original set are conserved, what are transformed, or what can we infer about one of the
representations by examining the other. Besides its theoretical appeal and intrinsic interest, we
consider that time series are a universal method of extracting information from dynamical systems
in any field of knowledge. It turns out that a number of interesting insights can be derived by using
this method and that the mathematical game has, therefore, various unexpected practical
applications as it opens the possibility of analyzing a time series (i.e. the outcome of a dynamical
process) from an alternative perspective. Finally, when the new representation belongs to a mature
and rigorous field, network science, the information encoded in such a representation can be
effectively processed and interpreted (Nuñez et al., 2012; Strozzi et al., 2009).
Many techniques have been proposed, based on concepts such as correlations, phase-space
reconstructions, recurrence analysis, transition probabilities (a list of all the proposed maps can be
found in Donner et al., 2010 and references therein). All these have shown that different features of
a time series are be mapped onto networks with distinct topological properties, thus suggesting the
possibility to distinguish properties of time series using network measures (Campanharo et al.,
2011; Donner et al., 2010; Nuñez et al., 2012; Yang & Yang, 2008).
Probably the simplest, conceptually and computationally, method is the one proposed by Lacasa et
al. (Lacasa et al., 2008; Nuñez et al., 2012): the visibility algorithm. By using this technique it has
been show that a time series structure is inherited in the associated graph, such that periodic,
random, and fractal series map into networks with different topologies (random exponential or
scale-free). Therefore, a visibility graph allows applying methods of complex network analysis for
characterizing time series in a simple way. So far, a number of studies have been published in fields
of stock market indices, exchange rates, macroeconomic indices, human behaviors, occurrence of
hurricanes, or dissipation rates in turbulent systems.
Aim of this paper is to present this type of analysis applied to a tourism destination. A time series of
overnight stays for a case destination is converted into a graph (network) by using the visibility
graph approach. Then the main topological properties of this graph are examined, namely, the
degree distribution, the clustering coefficient, the average path length, the community structure and
so on. The comparison with networks obtained by applying the same method to well known simple,
periodic, complex and chaotic systems allow us to better frame the main properties of a TD.
The contribution of this work is mainly methodological. It shows how a relatively simple technique
can be applied to a tourism system and can allow deriving important insights into its dynamics. This
can have important implications for academics and practitioners interested in enriching their
toolsets in order to better assess feasibility and effects of strategy and policy formulations or to
analyze and explain the phenomena relating to the behavior and development of tourism systems.
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