Related papers: Hamiltonian Dynamics of Preferential Attachment
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…
In this paper, we propose a growing random complex network model, which we call context dependent preferential attachment model (CDPAM), when the preference of a new node to get attached to old nodes is determined by the local and global…
Preferential attachment is a central paradigm in the theory of complex networks. In this contribution we consider various generalizations of preferential attachment including for example node removal and edge rewiring. We demonstrate that…
We discuss a model for evolutionary game dynamics in a growing, network-structured population. In our model, new players can either make connections to random preexisting players or preferentially attach to those that have been successful…
We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural…
We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…
The preferential attachment model is a natural and popular random graph model for a growing network that contains very well-connected ``hubs''. We study the higher-order connectivity of such a network by investigating the topological…
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…
Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…
Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like Trophic Analysis and non-normality. We propose a simple growing network model where the…
We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation…
Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…
In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of "commonly accepted beliefs" seems rarely studied. In this…