This paper addresses the simulation of the dynamics of complex systems by using hierarchical graph and multi-agent system. A complex system is composed of numerous interacting parts that can be described recursively. First we summarize the hierarchical aspect of the complex system. We then present a description of hierarchical graph as a data structure for structural modeling in parallel with d...

We study a discrete diffusion process introduced in some combinatorial games called FLOODIT and MADVIRUS that can be played online [1, 2] and whose computational complexity has been recently studied [3, 4]. The flooding dynamics used in those games can be defined for any colored graph. It is shown in [5] that studying this dynamics directly on general graph is a valuable approach to understand ...

A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

In the well-known discrete modeling framework developed by R. Thomas, the structure of a biological regulatory network is captured in an interaction graph, which, together with a set of Boolean parameters, gives rise to a state transition graph describing all possible dynamical behaviors. For complex networks the analysis of the dynamics becomes more and more difficult, and efficient methods to...

In previous work, we have introduced a "linear framework" for time-scale separation in biochemical systems, which is based on a labelled, directed graph, G, and an associated linear differential equation, dx/dt = L(G) ∙ x, where L(G) is the Laplacian matrix of G. Biochemical nonlinearity is encoded in the graph labels. Many central results in molecular biology can be systematically derived with...

The simulation of fluid dynamics, typically by numerically solving partial differential equations, is an essential tool in many areas science and engineering. However, the high computational cost can limit application practice may prohibit exploring large parameter spaces. Recent deep-learning approaches have demonstrated potential to yield surrogate models for dynamics. While such exhibit lowe...

In this work some preliminary numerical results obtained by large scale simulations of the sequential dynamics of a neural network model for the graph bisection problem on random geometrically connected graphs are presented. It can be concluded that the sequential dynamic is a low cost, effective and very fast local minima optimization heuristic for the Graph Bisection Problem.

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.