Related papers: Structural properties of spatially embedded networ…
Some features of random networks with excitable nodes that are embeddable in the Euclidean space are not describable in terms of the conventional integrate and fire model (IFM) alone, and some further details should be involved. In the…
Cascading failures constitute an important vulnerability of interconnected systems. Here we focus on the study of such failures on networks in which the connectivity of nodes is constrained by geographical distance. Specifically, we use…
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to…
One of the most important features of spatial networks such as transportation networks, power grids, Internet, neural networks, is the existence of a cost associated with the length of links. Such a cost has a profound influence on the…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
We implement molecular dynamics simulations in canonical ensemble to study the effect of confinement on a $2d$ crystal of point particles interacting with an inverse power law potential proportional to $r^{-12}$ in a narrow channel. This…
In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and…
Many real world complex systems such as infrastructure, communication and transportation networks are embedded in space, where entities of one system may depend on entities of other systems. These systems are subject to geographically…
We study the quantum statistical electronic properties of random networks which inherently lack a fixed spatial dimension. We use tools like the density of states (DOS) and the inverse participation ratio(IPR) to uncover various phenomena,…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary timescales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of…
In this paper we consider spatial networks that realize a balance between an infrastructure cost (the cost of wire needed to connect the network in space) and communication efficiency, measured by average shortest pathlength. A global…