Statistical properties of sampled networks

Graph sampling allows mining a small representative subgraph from a big graph. Sampling algorithms deploy different strategies to replicate the properties of a given graph in the sampled graph. In this study, we provide a comprehensive empirical characterization of five graph sampling algorithms on six properties of a graph including degree, clustering coefficient, path length, global clustering coefficient, assortativity, and modularity. We extract samples from fifteen graph...

In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most real situations, only limited sub-structures of entire networks are available, and therefore the reliability of the order relationships in sampled networks requires investigation. With a set of randomly sampled nodes from the underlying orig...

Many real-world networks are prohibitively large for data retrieval, storage and analysis of all of its nodes and links. Understanding the structure and dynamics of these networks entails creating a smaller representative sample of the full graph while preserving its relevant topological properties. In this report, we show that graph sampling algorithms currently proposed in the literature are not able to preserve network properties even with sample sizes containing as many a...

We study the statistical properties of the sampled networks by a random walker. We compare topological properties of the sampled networks such as degree distribution, degree-degree correlation, and clustering coefficient with those of the original networks. From the numerical results, we find that most of topological properties of the sampled networks are almost the same as those of the original networks for $\gamma \lesssim 3$. In contrast, we find that the degree distributi...

The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools and procedures to analyse the statistical properties of networks defined by arbitrary degree distributions and other constraints. Doing so reveals the highly likely properties, and some unrecognised richness, of scale-free networks, and cast...

The sampling method has been paid much attention in the field of complex network in general and statistical physics in particular. This paper presents two new sampling methods based on the perspective that a small part of vertices with high node degree can possess the most structure information of a network. The two proposed sampling methods are efficient in sampling the nodes with high degree. The first new sampling method is improved on the basis of the stratified random sa...

In the past few years, the storage and analysis of large-scale and fast evolving networks present a great challenge. Therefore, a number of different techniques have been proposed for sampling large networks. In general, network exploration techniques approximate the original networks more accurately than random node and link selection. Yet, link selection with additional subgraph induction step outperforms most other techniques. In this paper, we apply subgraph induction als...

From social networks to P2P systems, network sampling arises in many settings. We present a detailed study on the nature of biases in network sampling strategies to shed light on how best to sample from networks. We investigate connections between specific biases and various measures of structural representativeness. We show that certain biases are, in fact, beneficial for many applications, as they "push" the sampling process towards inclusion of desired properties. Finally,...

We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling. Here we derive a necessary and sufficient condition that guarantees that the degree distribution of the subnet and the true network belong to the same family of probability distributions. For completely random sampling of nodes we find tha...

We use mathematical methods from the theory of tailored random graphs to study systematically the effects of sampling on topological features of large biological signalling networks. Our aim in doing so is to increase our quantitative understanding of the relation between true biological networks and the imperfect and often biased samples of these networks that are reported in public data repositories and used by biomedical scientists. We derive exact explicit formulae for de...