Related papers: Characterizing network topology using first-passag…
We propose a novel network measure of topological invariants, called small-worldness, for identifying topological phase transitions of quantum and classical spin models. Small-worldness is usually defined in the study of social networks…
Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such…
Temporal network analysis and time evolution of network characteristics are powerful tools in describing the changing topology of dynamic networks. This paper uses such approaches to better visualize and provide analytical measures for the…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an…
In the previous chapters, we explored the effects of resetting on networks considering one and two nodes. In this chapter, we will describe a generalization of random walks with resetting to an arbitrary number of nodes $\mathcal{M}$. In…
Transport processes on spatial networks are representative of a broad class of real world systems which, rather than being independent, are typically interdependent. We propose a measure of utility to capture key features that arise when…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
Various graph algorithms have been developed with multiple random walks, the movement of several independent random walkers on a graph. Designing an efficient graph algorithm based on multiple random walks requires investigating multiple…
Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user's behavior coupled to the network dynamics and it effects should be…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
In general, the power-law degree distribution has profound influence on various dynamical processes defined on scale-free networks. In this paper, we will show that power-law degree distribution alone does not suffice to characterize the…
We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition…
We study navigation with limited information in networks and demonstrate that many real-world networks have a structure which can be described as favoring communication at short distance at the cost of constraining communication at long…
Network science has emerged as a powerful tool through which we can study the higher-order architectural properties of the world around us. How human learners exploit this information remains an essential question. Here, we focus on the…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
Previous work shows that the mean first-passage time (MFPT) for random walks to a given hub node (node with maximum degree) in uncorrelated random scale-free networks is closely related to the exponent $\gamma$ of power-law degree…
Two important aspects of the Internet, namely the properties of its topology and the characteristics of its data traffic, have attracted growing attention of the physics community. My thesis has considered problems of both aspects. First I…
Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…
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…