Related papers: Enhanced Flow in Small-World Networks
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They usually contain loops whose significance for the stability and robustness of the network is well documented. However,…
Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these…
We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social…
Strong resilience properties of dynamical flow networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the inflow at a non-destination node gets split among its outgoing links is…
Mobile multi-hop ad hoc networks allow establishing local groups of communicating devices in a self-organizing way. However, in a global setting such networks fail to work properly due to network partitioning. Providing that devices are…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…
In this report we show that in a planar exponentially growing network consisting of $N$ nodes, congestion scales as $O(N^2/\log(N))$ independently of how flows may be routed. This is in contrast to the $O(N^{3/2})$ scaling of congestion in…
Given a public transportation network of stations and connections, we want to find a minimum subset of stations such that each connection runs through a selected station. Although this problem is NP-hard in general, real-world instances are…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Training large and highly accurate deep learning (DL) models is computationally costly. This cost is in great part due to the excessive number of trained parameters, which are well-known to be redundant and compressible for the execution…
In this paper, we derive a topological pattern of urban street networks using a large sample (the largest so far to the best of our knowledge) of 40 U.S. cities and a few more from elsewhere of different sizes. It is found that all the…
The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and "Pseudo-Darwinian" strategy. At each evolution step and regarding the selected strategy, one removes either a…
A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, a long-range connection is randomly added to each node $i$ of a square lattice,…
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by…
One abstract method for the study of network transportation is proposed in this paper. By interpolating the properties of the edges that constitute network into the two leading parameters of the nodes, this method can abstract the…
Suppose that under the action of gravity, liquid drains through the unit $d$-cube via a minimal-length network of channels constrained to pass through random sites and to flow with nonnegative component in one of the canonical orthogonal…