Related papers: Network connectivity through small openings
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
We consider the probability that a dense wireless network confined within a given convex geometry is fully connected. We exploit a recently reported theory to develop a systematic methodology for analytically characterizing the connectivity…
Connectivity is one of the most fundamental properties of wireless multi-hop networks. A network is said to be connected if there is a path between any pair of nodes. A convenient way to study the connectivity of a random network is by…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…
In this paper, we study the problem of constructing a network by observing ordered connectivity constraints, which we define herein. These ordered constraints are made to capture realistic properties of real-world problems that are not…
Recent research has demonstrated the importance of boundary effects on the overall connection probability of wireless networks but has largely focused on convex deployment regions. We consider here a scenario of practical importance to…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
A simple and accurate relationship is demonstrated that links the average shortest path, nodes, and edges in a complex network. This relationship takes advantage of the concept of link density and shows a large improvement in fitting…
We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…
We employ the mathematical programming approach in conjunction with the graph theory to study the structure of correspondent banking networks. Optimizing the network requires decisions to be made to onboard, terminate or restrict the bank…
One of the most intriguing findings in the structure of neural network landscape is the phenomenon of mode connectivity: For two typical global minima, there exists a path connecting them without barrier. This concept of mode connectivity…
Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated to paths of…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…