Related papers: Mapping Sandpiles to Complex Networks
The vulnerability of an isolated network to cascades is fundamentally affected by its interactions with other networks. Motivated by failures cascading among electrical grids, we study the Bak-Tang-Wiesenfeld sandpile model on two…
Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here,…
In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy…
In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the…
A two state sandpile model with preferential sand distribution is developed and studied numerically on scale free networks with power-law degree ($k$) distribution, {\em i.e.}: $P_k\sim k^{-\alpha}$. In this model, upon toppling of a…
We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
We analyze the correlation between randomly chosen edge weights on neighboring edges in a directed graph. This shared-endpoint correlation controls the expected organization of randomly drawn edge flows when the flow on each edge is…
Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…
The development of algorithms for enhancing the resilience and efficiency of the power grid requires performance evaluation with real topologies of power transmission networks. However, due to security reasons, such topologies and…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Many mobile networks are represented as graphs to obtain insight to their connectivity and transmission properties. Among these properties centrality resilience, that is, how well centralities, such as closeness and betweennesss, are…
The widespread relevance of increasingly complex networks requires methods to extract meaningful coarse-grained representations of such systems. For undirected graphs, standard community detection methods use criteria largely based on…
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…
Graph Neural Networks (GNNs) have achieved tremendous success in various real-world applications due to their strong ability in graph representation learning. GNNs explore the graph structure and node features by aggregating and…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…