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Existing works on distributed consensus explore linear iterations based on reversible Markov chains, which contribute to the slow convergence of the algorithms. It has been observed that by overcoming the diffusive behavior of reversible…
The proliferation of social media platforms, recommender systems, and their joint societal impacts have prompted significant interest in opinion formation and evolution within social networks. We study how local edge dynamics can drive…
We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great…
Neural networks are not learning optimal decision boundaries. We show that decision boundaries are situated in areas of low training data density. They are impacted by few training samples which can easily lead to overfitting. We provide a…
We consider $N$ counters taking integer values which are subject to the following dynamics. At every time, a pair of distinct counters is chosen uniformly at random and their states are updated according to the following rule. If the states…
We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks…
Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by…
We introduce a new metric for collections of aged paths and a robust set of criteria for compactness for a set of collection of aged paths in the topology corresponding to this metric. We show that the distribution of stable webs ($1<…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
We study information aggregation in networks when agents interact to learn a binary state of the world. Initially each agent privately observes an independent signal which is "correct" with probability $\frac{1}{2}+\delta$ for some $\delta…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
We introduce and study the reverse voter model, a dynamics for spin variables similar to the well-known voter dynamics. The difference is in the way neighbors influence each other: once a node is selected and one among its neighbors chosen,…
In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is…
Assortativity, i.e. the tendency of a vertex to bond with another based on their similarity, such as degree, is an important network characteristic that is well-known to be relevant for the network's robustness against attacks. Commonly it…
Heterogeneity is a key aspect of complex networks, often emerging by looking at the distribution of node properties, from the milestone observations on the degree to the recent developments in mixing pattern estimation. Mixing patterns, in…
Synchronization in dynamical systems on directed weighted networks is often associated with stronger coupling and denser interactions. This paper shows that the opposite can also occur: weakening selected edges may increase the generalized…
Representation learning of static and more recently dynamically evolving graphs has gained noticeable attention. Existing approaches for modelling graph dynamics focus extensively on the evolution of individual nodes independently of the…
The social ranking is a recently proposed framework for evaluating the power of individuals according to the performance ranking of their coalitions. Although its origin can be traced to the classical power indices in simple games, social…
We study a mathematical model of social diffusion on a symmetric weighted network where individual nodes' states gradually assimilate to local social norms made by their neighbors' average states. Unlike physical diffusion, this process is…