Related papers: Vertex labeling and routing in expanded Apollonian…
In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called {\bf Random Apollonian Networks}(RAN) as they can be considered…
The possibility to identify the nature (e.g. random or scale free) of complex networks while performing respective random walks is investigated with respect to autonomous agents based on Bayesian decision theory and humans navigating…
When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
Alternative paths in a network play an important role in its functionality as they can maintain the information flow under node/link failures. In this paper we explore the navigation of a network taking into account the alternative paths…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…
We introduce an informative labeling algorithm for the vertices of a family of Koch networks. Each of the labels is consisted of two parts, the precise position and the time adding to Koch networks. The shortest path routing between any two…
An adjacency labeling scheme is a method that assigns labels to the vertices of a graph such that adjacency between vertices can be inferred directly from the assigned label, without using a centralized data structure. We devise adjacency…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
In this article, we investigate several properties of high-dimensional random Apollonian networks (HDRANs), including two types of degree profiles, the small-world effect (clustering property), sparsity, and three distance-based metrics.…
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…
Small world models are networks consisting of many local links and fewer long range 'shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution…
Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of…
Evolutionary game theory is employed to study topological conditions of scale-free networks for the evolution of cooperation. We show that Apollonian Networks (ANs) are perfect scale-free networks, on which cooperation can spread to all…
Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
We generalize the non-abelianization of Gaiotto-Moore-Neitzke from the case of $SL(n)$ and $GL(n)$ to arbitrary reductive algebraic groups. This gives a map between a moduli space of certain $N$-shifted weakly $W$-equivariant $T$-local…
We propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…