The Network Journal Club meets weekly to discuss interesting, recent papers mostly in the field of complex networks, although occasionally we will select papers related to complex systems in general. The first half an hour is reserved for the speaker to guide the attendants through the paper and the remaining half an hour is meant for informal discussions. Anyone interested in the current paper is welcome to attend.
Speaker: Marya Bazzi
Title: Community structure in financial asset correlation networks
Abstract: We investigate whether modularity maximization can help identify and track groups of strongly correlated financial assets in time. Intuitively, communities are groups of nodes that are `more strongly' connected to each other than to nodes in the rest of the network. Modularity maximization is a popular method for detecting communities in networks. In this method, the actual network is compared to a null network: the `expected network' under a specied null model. Given a choice of null model, the modularity maximization problem consists of partitioning the network into groups of nodes such that the sum of edge weights within groups in the actual network is maximally larger than the sum of edge weights within groups in the null network.
We formulate the modularity maximization problem in a `multilayer framework' and use the Reichardt-Bornholdt multiresolution formulation of modularity to study multiscale community structure in temporal networks of asset correlations. Focusing first on the choice of null model, we consider the modularity maximization problem on each layer independently as a special case of the multilayer framework. We show that the standard Newman-Girvan choice of null model in network analysis can introduce signicant sample biases in the interpretation of the multiscale community structure of a network and argue that a uniform null model is a more adequate choice of null model for the question under investigation. We then show how introducing interlayer coupling between consecutive time layers can help identify and distinguish temporal changes in evolving clusters. Finally, we discuss some implementation issues the Louvain algorithm, a popular heuristic used in modularity maximization, faces with this type of coupling and we suggest ways to mitigate them.