Related papers: Geodesic Length Distribution in Sparse Network Ens…

Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property,…

Geodesic distance, sometimes called shortest path length, has proven useful in a great variety of applications, such as information retrieval on networks including treelike networked models. Here, our goal is to analytically determine the…

Statistical ensembles of networks, i.e., probability spaces of all networks that are consistent with given aggregate statistics, have become instrumental in the analysis of complex networks. Their numerical and analytical study provides the…

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…

Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…

In several applications in distributed systems, an important design criterion is ensuring that the network is sparse, i.e., does not contain too many edges, while achieving reliable connectivity. Sparsity ensures communication overhead…

A set S of vertices of a graph G is a geodesic transversal of G if every maximal geodesic of G contains at least one vertex of S. We determine a smallest geodesic transversal in certain interconnection networks such as mesh of trees, and…

We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…

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…

In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense subtructures in otherwise sparse graphs (e.g. the World Wide Web or social networks); these might…

This paper describes a new approach to the problem of the structural research of clusters based on the theory of geodetic and k-geodetic graphs. We firmly believe that this same approach can be used when solving problems of correlation…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…

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…

We study the statistical properties of geodesics, i.e. paths of minimal length, in large random planar quadrangulations. We extend Schaeffer's well-labeled tree bijection to the case of quadrangulations with a marked geodesic, leading to…

Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we…

Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few…

The objective of this paper is to study the characteristics (geometric and otherwise) of very large attribute based undirected networks. Real-world networks are often very large and fast evolving. Their analysis and understanding present a…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…

We consider geodesic nets (critical points of a length functional on the space of embedded graphs) on doubled polygons (topological 2-spheres endowed with a flat metric away from finitely many cone singularities). We use the theorem of…