Motif formation and emergence of mesoscopic structure in complex networks
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Network structures can encode information from datasets that have a natural representation in terms of networks, for example datasets describing collaborations or social relations among individuals in science or society, as well as from data that can be mapped into graphs due to their intrinsic correlations, such as time series or images. Developing models and algorithms to characterise the structure of complex networks at the micro and mesoscale is thus of fundamental importance to extract relevant information from and to understand real world complex data and systems. In this thesis we will investigate how modularity, a mesoscopic feature observed almost universally in real world complex networks can emerge, and how this phenomenon is related to the appearance of a particular type of network motif, the triad. We will shed light on the role that motifs play in shaping the mesoscale structure of complex networks by considering two special classes of networks, multiplex networks, that describe complex systems where interactions of different nature are involved, and visibility graphs, a family of graphs that can be extracted from the time series of dynamical processes. This thesis is based on the research papers listed below, in particular on the first five, published between 2014 and 2016: 1. Bianconi, G., Darst R. K., Iacovacci J., Fortunato S., Triadic closure as a basic generating mechanism of communities in complex networks, Phys. Rev. E 90 (4), 042806 (2014). 2. Iacovacci J., Wu Z., Bianconi G., Mesoscopic structures reveal the network between the layers of multiplex data sets, Phys. Rev. E. 92 (4), 042806 (2015). 3. Battiston F., Iacovacci J., Nicosia V., Bianconi G., Latora V., Emergence of multiplex communities in collaboration networks, PloS one 11 (1), e0147451 (2016). 4. Iacovacci J., Lacasa L., Sequential visibility-graph motifs, Phys. Rev. E. 93 (4), 042309 (2016). 5. Iacovacci J., Lacasa L., Sequential motif pro le of natural visibility-graphs, Phys. Rev. E. 94 (5), 052309 (2016). 6. Iacovacci J., Bianconi G., Extracting information from multiplex networks, Chaos: An Interdisciplinary Journal of Nonlinear Science 26 (6), 065306 (2016). 7. Iacovacci J., Rahmede C., Arenas A., Bianconi G., Functional Multiplex PageRank, EPL (Europhysics Letters) 116(2), 28004 (2016). 8. Lacasa L, Iacovacci J., Visibility graphs of random scalar elds and spatial data, arXiv preprint arXiv:1702.07813 (2017). 9. Rahmede C, Iacovacci J, Arenas A, Bianconi G., Centralities of Nodes and In infuences of Layers in Large Multiplex Network, arXiv preprint arXiv:1703.05833 (2017).
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