Scale-free networks as an epiphenomenon of memory

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key idea is that in many cases the process involves copying of properties of near neighbours in the network and this is a type of short random walk which in turn produce a natural preferential attachment mechanism. Applying this to networks of fi...

We propose dynamic scaling in temporal networks with heterogeneous activities and memory, and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim \textit{et al.}, Eur. Phys. J. B {\bf 88}, 315 (2015)]. Particularly, we focus on the interplay of the time resolution and memory in dynamic topologies. Through the random walk (RW) process, we investigate diffusion properties and topological cha...

Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local interactions non-trivial global phenomena can emerge as small-world properties or scale-free degree distributions. A simple model for the evolution of acquaintance networks highlights the essential dynamical ingredients necessary to obtain such...

At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral patterns. They rely on algorithms with a global view, significantly differing from biological neural networks, in which, to simulate information storage and retrieval processes, the limitations of centralized algorithms must be overcome. This ...

We study the influence of network topology on retrieval properties of recurrent neural networks, using replica techniques for diluted systems. The theory is presented for a network with an arbitrary degree distribution $p(k)$ and applied to power law distributions $p(k) \sim k^{-\gamma}$, i.e. to neural networks on scale-free graphs. A bifurcation analysis identifies phase boundaries between the paramagnetic phase and either a retrieval phase or a spin glass phase. Using a po...

A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two limiting cases and numerical simulations the phase diagram of the model is obtained. In the stationary limit, large network sizes, a phase transition from a network with finite average connectivity to a network with a power law distributio...

We introduce a simple one-parameter network growth algorithm which is able to reproduce a wide variety of realistic network structures but without having to invoke any global information about node degrees such as preferential-attachment probabilities. Scale-free networks arise at the transition point between quasi-random and quasi-ordered networks. We provide a detailed formalism which accurately describes the entire network range, including this critical point. Our formalis...

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most efficient for storage and retrieval of patterns by the entire network. However, in the scale-free case retrieval errors are not distributed uniformly: the portion of a pattern encoded by the subset of highly connected nodes is more robust a...

What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is introduced in this letter. At each time step, a new node is added to the network and connect to some existing nodes randomly, instead of "preferential attachment" introduced by Barab\'{a}si and Albert, and then the new node will connect with ...

The Hopfield network model and its generalizations were introduced as a model of associative, or content-addressable, memory. They were widely investigated both as a unsupervised learning method in artificial intelligence and as a model of biological neural dynamics in computational neuroscience. The complexity features of biological neural networks are attracting the interest of scientific community since the last two decades. More recently, concepts and tools borrowed from ...