Complex networks analysis from an edge perspective

by Andreia Sofia Monteiro Teixeira

PhD thesis presentation and discussion.

Date: 2019-Jul-02   Time: 14:30
Room: IST 4.41

Abstract: If we carefully observe our daily lives and the systems in which we
participate, we naturally perceive that everything is somehow connected. From
species evolution to social relations, acknowledging all the supply chain
systems we depend on, networks portray the simplest representation of these
systems.  Notwithstanding this simplicity, these networks often underlie
complex dynamics. Species and population evolution are subject to many complex
interactions. Individuals’ states – from individual choices, epidemic states,
strategic behaviors, opinions, among others – are influenced by social ties
and by the overall topology of interaction. These networks, called complex
networks, show a prevalence of certain features, which are shared between
completely different systems, thus defying the limits of the traditional
techniques of analysis and intriguing the research community.

In this thesis we aim to contribute to the study of the relationship between
structure and dynamics of these complex networks. Usually, the approaches to
study complex networks are centered on the importance of nodes. However, it is
our understanding that the edge-perspective analysis also provides fundamental
and complementary information on the structure and behavior of complex
networks. Given this, throughout this dissertation we approach complex
networks under an edge perspective, centering our attention on the properties
of the edges. In our contributions we provide new metrics, models, and
computational tools. We start by contributing with a new edge centrality
measure. Next, we focus on analyzing local patterns(or subgraphs) whose edges
contain informative labels, highlighting that sometimes observing only nodes
and edges, individually, is not enough to fully understand the dynamics and/or
the structure of a system. Finally, we argue that representing a system with a
single network is often insufficient to reproduce its behavior. Therefore, it
is necessary to consider networks at multiple scales, i.e. networks of
networks. In this context, we propose a new computational framework that
allows us to model and simulate a system represented as a network of networks.