SuperNoder: a tool to discover over-represented modular structures in networks

Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

We introduce simplicial persistence, a measure of time evolution of motifs in networks obtained from correlation filtering. We observe long memory in the evolution of structures, with a two power law decay regimes in the number of persistent simplicial complexes. Null models of the underlying time series are tested to investigate properties of the generative process and its evolutional constraints. Networks are generated with both a topological embedding network filtering technique called TMFG and by thresholding, showing that the TMFG method identifies high order structures throughout the market sample, where thresholding methods fail. The decay exponents of these long memory processes are used to characterise financial markets based on their efficiency and liquidity. We find that more liquid markets tend to have a slower persistence decay. This appears to be in contrast with the common understanding that efficient markets are more random. We argue that they are indeed less predictable for what concerns the dynamics of each single variable but they are more predictable for what concerns the collective evolution of the variables. This could imply higher fragility to systemic shocks.

Subgraphs of Interest Social Networks for Diffusion Dynamics Prediction

Finding the building blocks of real-world networks contributes to the understanding of their formation process and related dynamical processes, which is related to prediction and control tasks. We explore different types of social networks, demonstrating high structural variability, and aim to extract and see their minimal building blocks, which are able to reproduce supergraph structural and dynamical properties, so as to be appropriate for diffusion prediction for the whole graph on the base of its small subgraph. For this purpose, we determine topological and functional formal criteria and explore sampling techniques. Using the method that provides the best correspondence to both criteria, we explore the building blocks of interest networks. The best sampling method allows one to extract subgraphs of optimal 30 nodes, which reproduce path lengths, clustering, and degree particularities of an initial graph. The extracted subgraphs are different for the considered interest networks, and provide interesting material for the global dynamics exploration on the mesoscale base.