Related papers: Mapping Sandpiles to Complex Networks
We study a distributed consensus-based stochastic gradient descent (SGD) algorithm and show that the rate of convergence involves the spectral properties of two matrices: the standard spectral gap of a weight matrix from the network…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
We investigate saturation effects in susceptible-infected-susceptible (SIS) models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity…
Discrete-element simulations are used to monitor several micro-scale characteristics within a granular material, demonstrating their convergence during loading toward the critical state, their stationarity at the critical state, and the…
Understanding the importance of links in transmitting information in a network can provide ways to hinder or postpone ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. In this work, we propose a new…
Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and…
Centrality is a fundamental network property which ranks nodes by their structural importance. However, structural importance may not suffice to predict successful diffusions in a wide range of applications, such as word-of-mouth marketing…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
Influential nodes play a critical role in boosting or curbing spreading phenomena in complex networks. Numerous centrality measures have been proposed for identifying and ranking the nodes according to their importance. Classical centrality…
Semantic similarity measures (SSMs) refer to a set of algorithms used to quantify the similarity of two or more terms belonging to the same ontology. Ontology terms may be associated to concepts, for instance in computational biology gene…
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…
Nodes in networks may have one or more functions that determine their role in the system. As opposed to local proximity, which captures the local context of nodes, the role identity captures the functional "role" that nodes play in a…
We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a…
A fundamental problem in the study of networks is the identification of important nodes. This is typically achieved using centrality metrics, which rank nodes in terms of their position in the network. This approach works well for static…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
Spectroscopy infers the internal structure of physical systems by measuring their response to perturbations. We apply this principle to neural networks: perturbing the data distribution by upweighting a token $y$ in context $x$, we measure…
Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of…
Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…