Network Features in Complex Applications

The aim of this thesis is to show the potential of Graph Theory and Network Science applied in real-case scenarios. Indeed, there is a gap in the state-of-art in combining mathematical theory with more practical applications such as helping the Law Enforcement Agencies (LEAs) to conduct their investigations, or in Deep Learning techniques which enable Artificial Neural Networks (ANNs) to work more efficiently. In particular, three main case studies on which evaluate the goodness of Social Network Analysis (SNA) tools were considered: (i) Criminal Networks Analysis, (ii) Networks Resilience, and (iii) ANN topology.

We have addressed two typical problems in dealing with criminal networks: (i) how to efficiently slow down the information spreading within the criminal organisation by prompt and targeted investigative operations from LEAs and (ii) what is the impact of missing data during LEAs investigation.

In the first case, we identified the appropriate centrality metric to effectively identify the criminals to be arrested, showing how, by neutralising only 5% of the top-ranking affiliates, the network connectivity dropped by 70%.

In the second case, we simulated the missing data problem by pruning some criminal networks by removing nodes or links and compared these networks against the originals considering four metrics to compute graph similarities. We discovered that a negligible error (i.e., 30% difference from the real network) was detected when, for example, some wiretaps are missing. On the other hand, it is crucial to investigate the suspects in a timely fashion, since any exclusion of suspects from an investigation may lead to significant errors (i.e., 80% difference).

Next, we defined a new approach for simulating network resilience by a probabilistic failure model. Indeed, while the classical approach for removing nodes was always successful, such an assumption was not realistic. Thus, we defined some models simulating the scenario in which nodes oppose resistance against removal. Once identified the centrality metric that on average, generates the biggest damage in the connectivity of the networks under scrutiny, we have compared our outcomes against the classical node removal approach, by ranking the nodes according to the same centrality metric, which confirmed our intuition.

Lastly, we adopted SNA techniques to analyse ANNs. In particular, we moved a step forward from earlier works because not only did our experiments confirm the efficiency arising from training sparse ANNs, but they also managed to further exploit sparsity through a better tuned algorithm, featuring increased speed at a negligible accuracy loss. We focused on the role of the parameter used to fine-tune the training phase of Sparse ANNs. Our intuition has been that this step can be avoided as the accuracy loss is negligible and, as a consequence, the execution time is significantly reduced. Yet, it is evident that Network Science algorithms, by keeping sparsity in ANNs, are a promising direction for accelerating their training processes.

All these studies pave the way for a range of unexplored possibilities for an effective use of Network Science at the service of society.

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