Related papers: Blume-Emery-Griffiths model on Random Graphs
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
In network data analysis, summary statistics of a network can provide us with meaningful insight into the structure of the network. The average clustering coefficient is one of the most popular and widely used network statistics. In this…
The time evolution of the extremely diluted Blume-Emery-Griffiths neural network model is studied, and a detailed equilibrium phase diagram is obtained exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity phases.…
We introduce a measure of {\em greedy connectivity} for geographical networks (graphs embedded in space) and where the search for connecting paths relies only on local information, such as a node's location and that of its neighbors.…
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…
The phase-diagram of the two-dimensional Blume-Capel model with a random crystal field is investigated within the framework of a real-space renormalization group approximation. Our results suggest that, for any amount of randomness, the…
Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks…
This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes,…
We study the connectivity properties of random Bluetooth graphs that model certain "ad hoc" wireless networks. The graphs are obtained as "irrigation subgraphs" of the well-known random geometric graph model. There are two parameters that…
We construct and analyze a random graph model for discrete choice with social interaction and several groups of equal size. We concentrate on the case of two groups of equal sizes and we allow the interaction strength within a group to…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Group-based brain connectivity networks have great appeal for researchers interested in gaining further insight into complex brain function and how it changes across different mental states and disease conditions. Accurately constructing…
We consider the edge-triangle model (or Strauss model), and focus on the asymptotic behavior of the triangle density when the size of the graph increases to infinity. This random graph belongs to the class of exponential random graphs,…