Related papers: Self-avoiding walks and connective constants in sm…
Neural circuits must balance local connectivity constraints against the need for global integration. Here we introduce a minimal wiring rule motivated by synaptic crowding: as a neuron accumulates incoming connections, each additional…
We develop an analytical approach which provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
Many real life networks, such as the World Wide Web, transportation systems, biological or social networks, achieve both a strong local clustering (nodes have many mutual neighbors) and a small diameter (maximum distance between any two…
We use the recently conjectured exact $S$-matrix of the massive ${\rm O}(n)$ model to derive its form factors and ground state energy. This information is then used in the limit $n\to0$ to obtain quantitative results for various universal…
Let $G=(V,E)$ be a $d$-regular graph on $n$ vertices and let $\mu_0$ be a probability measure on $V$. The act of moving to a randomly chosen neighbor leads to a sequence of probability measures supported on $V$ given by $\mu_{k+1} = A…
Soft Random Geometric Graphs (SRGGs) have been widely applied to various models including those of wireless sensor, communication, social and neural networks. SRGGs are constructed by randomly placing nodes in some space and making pairwise…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
Consider the following routing problem in the context of a large scale network $G$, with particular interest paid to power law networks, although our results do not assume a particular degree distribution. A small number of nodes want to…
Most agent-based models include a social network that describes the structure of interactions within the artificial population. Because of the dramatic impact of this structure on the simulated dynamics, modelers create this network for it…
The self averaging properties of conductance $g$ are explored in random resistor networks with a broad distribution of bond strengths $P(g)\simg^{\mu-1}$. Distributions of equivalent conductances are estimated numerically on hierarchical…
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…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…
The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…
A growing self-avoiding walk (GSAW) is a stochastic process that starts from the origin on a lattice and grows by occupying an unoccupied adjacent lattice site at random. A sufficiently long GSAW will reach a state in which all adjacent…
Qualitatively, some real networks in the brain could be characterized as 'small worlds', in the sense that the structure of their connections is intermediate between the extremes of an orderly geometric arrangement and of a…
By modifying the automaton used by P{\"o}nitz and Tittman [4], and considering loops of length up to 26, we obtain 2.662343 as an upper bound for the connective constant in the lattice Z 2 .