A generative model for sparse, evolving digraphs

Generating graphs that are similar to real ones is an open problem, while the similarity notion is quite elusive and hard to formalize. In this paper, we focus on sparse digraphs and propose SDG, an algorithm that aims at generating graphs similar to real ones. Since real graphs are evolving and this evolution is important to study in order to understand the underlying dynamical system, we tackle the problem of generating series of graphs. We propose SEDGE, an algorithm meant to generate series of graphs similar to a real series. SEDGE is an extension of SDG. We consider graphs that are representations of software programs and show experimentally that our approach outperforms other existing approaches. Experiments show the performance of both algorithms

Functional and spatial rewiring jointly generate convergent-divergent units in self-organizing networks

Self-organization through adaptive rewiring of random neural networks generates brain-like topologies comprising modular small-world structures with rich club effects, merely as the product of optimizing the network topology. In the nervous system, spatial organization is optimized no less by rewiring, through minimizing wiring distance and maximizing spatially aligned wiring layouts. We show that such spatial organization principles interact constructively with adaptive rewiring, contributing to establish the networks' connectedness and modular structures. We use an evolving neural network model with weighted and directed connections, in which neural traffic flow is based on consensus and advection dynamics, to show that wiring cost minimization supports adaptive rewiring in creating convergent-divergent unit structures. Convergent-divergent units consist of a convergent input-hub, connected to a divergent output-hub via subnetworks of intermediate nodes, which may function as the computational core of the unit. The prominence of minimizing wiring distance in the dynamic evolution of the network determines the extent to which the core is encapsulated from the rest of the network, i.e., the context-sensitivity of its computations. This corresponds to the central role convergent-divergent units play in establishing context-sensitivity in neuronal information processing

Local Algorithms for Finding Densely Connected Clusters

Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a vertex set of low conductance, there has been a sequence of recent studies that highlight the importance of the inter-connection between clusters when analysing real-world datasets. Following this line of research, in this work we study local algorithms for finding a pair of vertex sets defined with respect to their inter-connection and their relationship with the rest of the graph. The key to our analysis is a new reduction technique that relates the structure of multiple sets to a single vertex set in the reduced graph. Among many potential applications, we show that our algorithms successfully recover densely connected clusters in the Interstate Disputes Dataset and the US Migration Dataset.Comment: This work is accepted at ICML'21 for a long presentatio

Controllability in complex brain networks

Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures. Recently it has been proposed to characterize brain networks in terms of their "controllability", drawing on concepts and methods of control theory. The thesis will review the control theory for networks and its application in neuroscience. In particular, the study will highlight important limitations and some warning and caveats in the brain controllability framework.ope