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Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…
This work is concerned with the intricate interplay between node or pore pressures and connection or throat conductivities in flow or pore networks. A setting similar to pore networks is given by fracture networks. Recently, a non-local…
Any network studied in the literature is inevitably just a sampled representative of its real-world analogue. Additionally, network sampling is lately often applied to large networks to allow for their faster and more efficient analysis.…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
Landscapes that are rhythmically dissected by natural drainage channels exist in various geologic and climatic settings. Such landscapes are characterized by a length-scale for the lateral spacing between channels. We observe a small-scale…
We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability…
We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The…
The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we…
We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…
We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an…
A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed.…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…