1. Opinion and consensus dynamics in
tourism digital ecosystems
Rodolfo Baggio
Bocconi University, Italy
Giacomo Del Chiappa
University of Sassari and CRENoS, Italy
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Slide Number 1

2. Background (1)
The Web is not simply a technological
manifestation but a reflection of
social structures and processes
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3. Background (2)
Tourism destination : digital business ecosystem
– dynamically interlinked real and virtual agents
– digital components are intelligent, active and adaptive
organisms
– system is in continuous evolution (perpetual beta)
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4. Efficiency
Tourism digital ecosystem
System structure affects functions
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5. Background (3)
• Collaboration, harmonization and coordination of
stakeholders’ views pivotal for effective &
competitive tourism development
• Enforced through consensus building
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6. Objectives
• Reconfirm, on more solid bases, structural
interdependence of real & virtual components in
a tourism digital ecosystem
• Investigate how digital ecosystem topology affects
opinion sharing & consensus development among
stakeholders
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7. Materials
Livigno
Elba
Gallura
• Three Italian destinations
– Elba, Gallura, Livigno
– Similar size ( 1000 firms)
– Similar tourism intensity
(500k tourists/year,
strong seasonality)
• Collected data & built
network
– core tourism operators +
websites
– links btw firms & websites
• also weighted
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8. Similar characteristics
& topology
Cumulative deg. distrib.
Materials
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9. Dynamic processes
• Information diffusion
– epidemiological models on network substrate;
– main parameter: infectivity τ
– infection process possible when τ > τC (critical threshold)
• Synchronization
– models consensus formation
– physical model by Kuramoto: system elements are coupled
oscillators, each with intrinsic frequency & characteristic phase
– main parameter: coupling K
– whole system synchronises when K > KC (critical coupling)
(i.e. all oscillators have same phase -> opinions are aligned)
• NB: critical values depend on system configuration
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10. Nets, matrices, eigenvalues & eigenvectors
• For a square (n n) matrix M, it is possible to find a scalar λ
and a vector xn 1 0 satisfying Mx = λx.
• λ, x are called eigenvalues & eigenvectors of M;
– a real symmetric n n matrix M has n real eigenvalues
– the set of distinct eigenvalues is called the spectrum of M
• Eigenvalues and eigenvectors “summarize” network topology
– eigenvalues: global information,
eigenvectors: local (nodal) information
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11. Methods
• Spectral analysis, i.e. analysis of the eigenvalues and
eigenvector of the adjacency & Laplacian matrices of
the 3 networks
– useful, and often computationally more efficient, way to
assess network main parameters
Adjacency matrix:
Laplacian matrix:
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12. Methods
Use 2 results from graph spectral theory:
• Fiedler vector: eigenvector associated with second
smallest Laplacian eigenvalue 2 renders algebraic
connectivity of the network
– large gaps in plot  separation between “communities”
• Spectral radius: largest eigenvalue of adjacency
matrix λN
– SIS epidemic diffusion in undirected graph:
critical threshold τC = 1/λN
– Synchronization: critical coupling KC 1/λN
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13. Results: topology
Fiedler vector
Artificial network w. 2
well separated modules
No trivial separation possible
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14. Results: diffusion & synchronization
• The values for whole ecosystems < those of single
components (minimum is for weighted networks)
NB: weights assigned to links considering probable cost of links
(RR=1, VR=2, VV=3)
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15. Concluding remarks
• Reconfirm that no trivial structural separation is
possible between real and virtual components in a
tourism system
• Combination of real and virtual elements in a single
integrated system provides a more efficient
substrate for the spreading of ideas or the reaching
of a consensus on some issue
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Slide Number 15