Related papers: A deterministic small-world network created by edg…

It has been observed that almost anyone is acquainted with almost anyone else through only a few intermediary links. This has been known as the small-world phenomenon. In this script we investigate this observation from a theoretical…

Communication networks show the small-world property of short paths, but the spreading dynamics in them turns out slow. We follow the time evolution of information propagation through communication networks by using the SI model with…

We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These…

We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the…

Economy, and consequently trade, is a fundamental part of human social organization which, until now, has not been studied within the network modelling framework. Networks are mathematical tools used in the modelling of a wide variety of…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

Dynamical processes on complex networks such as information propagation, innovation diffusion, cascading failures or epidemic spreading are highly affected by their underlying topologies as characterized by, for instance, degree-degree…

Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…

It is often desirable to assess how well a given dataset is described by a given model. In network science, for instance, one often wants to say that a given real-world network appears to come from a particular network model. In statistical…

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…

A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most…

We introduce a network growth model based on complete redirection: a new node randomly selects an existing target node, but attaches to a random neighbor of this target. For undirected networks, this simple growth rule generates unusual,…

Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…

In this paper, we introduce a conceptual framework that model human social networks as an undirected dot-product graph of independent individuals. Their relationships are only determined by a cost-benefit analysis, i.e. by maximizing an…

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…

We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be…

In this paper we introduce a new model of data packet transport, based on a stochastic approach with the aim of characterizing the load distribution on complex networks. Moreover we analyze the load standard deviation as an index of…

Many networks extent in space, may it be metric (e.g. geographic) or non-metric (ordinal). Spatial network growth, which depends on the distance between nodes, can generate a wide range of topologies from small-world to linear scale-free…

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…