Modelling and Analysis of Probabilistic Networks

As empirical data collection and inference is often an imperfect process, and many systems can be represented as networks, it is important to develop modelling and analysis methods for imperfect network data. The main focus of this dissertation is the probabilistic network model G = (V, E, p) in which each edge is associated with an independent existence probability. This model can be used to represent both collected data and our understanding about it in many applications such as biological and social network analysis. A probabilistic network with m probabilistic edges corresponds to 2m deterministic instances, known as possible worlds, and most of the existing network analysis measures can be represented as probability distributions. This introduces three challenges. The first challenge is to find methods to calculate or estimate the required measures with non-exponential computational time complexity. The second challenge arises due to the fact that many network analysis algorithms are designed to use single number measures such as degree and cannot deal with measures that are represented as probability distributions. Therefore, the second challenge in this field is to adapt network science algorithms such that they can utilise the information represented in measures’ probability distributions. The third challenge is the aggregation of information yielded from the analysis of possible worlds. This thesis has considered these three challenges. In particular, this thesis first scrutinises fundamental local measures in probabilistic networks. It proposes measures to compare nodes’ degree distributions and it introduces a method to estimate these measures. Moreover, it extends the concepts of ego network and ego betweenness to probabilistic networks, and proposes a method to estimate ego betweenness in this context. Second, this thesis focuses on the problem of probabilistic network sparsification which is a method to generate an alternative probabilistic network whose analysis is simpler than the original one. Third, this thesis studies for the first time the problem of overlapping community detection in probabilistic networks and proposes and compares different extensions of the clique percolation method for such networks.