| dc.description.abstract | Network science has provided useful answers to research questions in many fields, from
biology to social science, from ecology to urban science. The first analyses of networked
systems focused on binary networks, where only the topology of the connections were
considered. Soon network scientists started considering weighted networks, to represent
interactions with different strength, cost, or distance in space and time. Also, connections
are not fixed but change over time. This is why in more recent years, a lot of attention
has been devoted to temporal or time-varying networks.
We now entered the era of multi-layer networks, or multiplex networks, relational systems
whose units are connected by different relationships, with links of distinct types
embedded in different layers. Multiplexity has been observed in many contexts, from
social network analysis to economics, medicine and ecology. The new challenge consists
in applying the new tools of multiplex theory to unveil the richness associated to this
novel level of complexity. How do agents organise their interactions across layers? How
does this affect the dynamics of the system?
In the first part of the thesis, we provide a mathematical framework to deal with multiplex
networks. We suggest metrics to unveil multiplexity from basic node, layer and edge
properties to more complicated structure at the micro- and meso-scale, such as motifs,
communities and cores. Measures are validated through the analysis of real-world systems
such as social and collaboration networks, transportation systems and the human
brain.
In the second part of the thesis we focus on dynamical processes taking place on top of
multiplex networks, namely biased random walks, opinion dynamics, cultural dynamics
and evolutionary game theory. All these examples show how multiplexity is crucial to
determine the emergence of unexpected and instrinsically multiplex collective behavior,
opening novel perspectives for the field of non-linear dynamics on networks. | en_US |
