Prox is a stochastic method to map the local and global structures of real-world complex networks which are called Small Worlds. Prox transforms a graph into a Markov chain, the states of which are the nodes of the graph in question. Particles wander from one node to another within the graph by following the graph‟s edges. It is the dynamics of the particles‟ trajectories that map the structura...

Building occupancy simulation and estimation simulates the dynamics of occupants and estimates the real time spatial distribution of occupants in a building. It can benefit various applications like conserving energy, smart assist, building construction, crowd management, and emergency evacuation. Building occupancy simulation and estimation needs a simulation model and a data assimilation algo...

The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...

‎in this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $c_4$-free.‎

For a graph G and a unary graph operation X, there is a graph sequence {Gk} generated by G0 = G and Gk+1 = X(Gk). Let Sp(Gk) denote the set of normalized Laplacian eigenvalues of Gk. The set of limit points of ⋃∞ k=0 Sp(Gk), lim infk→∞ Sp(Gk) and lim supk→∞ Sp(Gk) are considered in this paper for graph sequences generated by two operations: subdivision and triangle extension. It is obtained tha...

Abstract This article is concerned with a general class of stochastic spatial models for the dynamics of opinions. Like in the voter model, individuals are located on the vertex set of a connected graph and update their opinion at a constant rate based on the opinion of their neighbors. However, unlike in the voter model, the set of opinions is represented by the set of vertices of another conn...

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure...

We explore the networks that yield the largest mean consensus time of voter models under different update rules. By analytical and numerical means, we show that the so-called lollipop graph, barbell graph, and double star graph maximise the mean consensus time under the update rules called the link dynamics, voter model, and invasion process, respectively. For each update rule, the largest mean...

We explore the networks that yield the largest mean consensus time of voter models under different update rules. By analytical and numerical means, we show that the so-called lollipop graph, barbell graph, and double-star graph maximize the mean consensus time under the update rules called the link dynamics, voter model, and invasion process, respectively. For each update rule, the largest mean...

In this paper we introduce a simple and mathematically tractable model of an asynchronous spiking neural network which to some extent generalizes the concept of a Boltzmann machine. In our model we let the units contain a certain (possibly unbounded) charge, which can be exchanged with other neurons under stochastic dynamics. The model admits a natural energy functional determined by weights as...