Related papers: Shortest paths govern fracture nucleation in therm…
Large networked systems are constantly exposed to local damages and failures that can alter their functionality. The knowledge of the structure of these systems is however often derived through sampling strategies whose effectiveness at…
In this paper we present an analytic study of sampled networks in the case of some important shortest-path sampling models. We present analytic formulas for the probability of edge discovery in the case of an evolving and a static network…
Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are,…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
Designing strong and robust bio-inspired structures requires an understanding of how function arises from the architecture and geometry of materials found in nature. We draw from trabecular bone, a lightweight bone tissue that exhibits a…
Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on…
Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and…
The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…
The overwhelming majority of survivable (fault-tolerant) network design models assume a uniform scenario set. Such a scenario set assumes that every subset of the network resources (edges or vertices) of a given cardinality $k$ comprises a…
Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional…
We propose a mapping from fracture systems consisting of intersecting fracture sheets in three dimensions to an abstract network consisting of nodes and links. This makes it possible to analyze fracture systems with the methods developed…
Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications.…
Fractal structure of shortest paths depends strongly on interresidue interaction cutoff distance. The dimensionality of shortest paths is calculated as a function of interaction cutoff distance. Shortest paths are self similar with a…
The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity in a given undirected graph. The problem is known to be NP-complete and W[2]-hard with respect to the desired eccentricity. We…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
In a network, the shortest paths between nodes are of great importance as they allow the fastest and strongest interaction between nodes. However measuring the shortest paths between all nodes in a large network is computationally…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…
Understanding how packets are routed in Internet is significantly important to Internet measurement and modeling. The conventional solution for route simulation is based on the assumption of unweighted shortest path. However, it has been…
The shortest-path percolation (SPP) model aims at describing the consumption and eventual exhaustion of a network's resources. Starting from a network containing a macroscopic connected component, random pairs of nodes are sequentially…