Tesi etd-09272021-123919 |
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Tipo di tesi
Tesi di laurea magistrale
Autore
MAGGIONI, EDOARDO
Indirizzo email
e.maggioni@studenti.unipi.it, edo.magg@me.com
URN
etd-09272021-123919
Titolo
Geometrical frustration and its effect in signed social networks
Dipartimento
FISICA
Corso di studi
FISICA
Relatori
relatore Prof. Schweitzer, Frank
correlatore Dott. Vaccario, Giacomo
supervisore Prof. Mannella, Riccardo
correlatore Dott. Vaccario, Giacomo
supervisore Prof. Mannella, Riccardo
Parole chiave
- geometrical frustration
- network
- signed network
- social system
- sociophysics
- structural balance theory
Data inizio appello
25/10/2021
Consultabilità
Tesi non consultabile
Riassunto
The thesis studies frustrated random networks and proposes a model for generating interactions from them.
In particular, the proposed model generates interaction patterns within social systems.
The thesis is divided into four parts.
1) We first introduce the necessary definitions and concepts from network theory, geometrical frustration in physics and balance theory in social science. With a network perspective, we abstract from the many different details of physical and social systems and focus instead on the shared elements: i) the nodes representing individuals (or particles) and ii) the signed links representing the relations between individuals (or interactions between particles).
Moreover, thanks to balance theory, we bridge the concepts of geometrical frustration from physics and cognitive dissonance in social science.
2) By taking a statistical physics approach, we introduce a pseudo-Hamiltonian function that quantifies the "cost" of a given set of signed dyadic relations in a system.
This function is composed of three different terms: the preference of having positive relations, the preference of being included in balanced triadic relations, and the preference to interact with nodes with similar characteristics.
We study these terms analytically and numerically to characterise the energy landscape and provide exact values of the energy levels.
3) Using the proposed pseudo-Hamiltonian, we develop a procedure to generate interactions within a social system.
By carefully analysing the pseudo-Hamiltonian, we find that it cannot be directly used to model the formation of social interactions.
Therefore, we modify the procedure by proposing a new set of rules.
We then analyse the topology of the networks that emerge by aggregating the generated interactions.
4) The last part of this thesis is devoted to the extensions and applications of the presented model.
We first discuss how to introduce a dynamic for signed dyadic relations by using a Lagrangian formulation.
Then we create a connection between our model and the Exponential family of Random Graph Models (ERGMs).
With this connection, we provide a way to infer the parameters of the presented model starting from real-world data.
In particular, the proposed model generates interaction patterns within social systems.
The thesis is divided into four parts.
1) We first introduce the necessary definitions and concepts from network theory, geometrical frustration in physics and balance theory in social science. With a network perspective, we abstract from the many different details of physical and social systems and focus instead on the shared elements: i) the nodes representing individuals (or particles) and ii) the signed links representing the relations between individuals (or interactions between particles).
Moreover, thanks to balance theory, we bridge the concepts of geometrical frustration from physics and cognitive dissonance in social science.
2) By taking a statistical physics approach, we introduce a pseudo-Hamiltonian function that quantifies the "cost" of a given set of signed dyadic relations in a system.
This function is composed of three different terms: the preference of having positive relations, the preference of being included in balanced triadic relations, and the preference to interact with nodes with similar characteristics.
We study these terms analytically and numerically to characterise the energy landscape and provide exact values of the energy levels.
3) Using the proposed pseudo-Hamiltonian, we develop a procedure to generate interactions within a social system.
By carefully analysing the pseudo-Hamiltonian, we find that it cannot be directly used to model the formation of social interactions.
Therefore, we modify the procedure by proposing a new set of rules.
We then analyse the topology of the networks that emerge by aggregating the generated interactions.
4) The last part of this thesis is devoted to the extensions and applications of the presented model.
We first discuss how to introduce a dynamic for signed dyadic relations by using a Lagrangian formulation.
Then we create a connection between our model and the Exponential family of Random Graph Models (ERGMs).
With this connection, we provide a way to infer the parameters of the presented model starting from real-world data.
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