Related papers: Sampling from naturally truncated power laws: The …

Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of…

It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main argument that power laws are otherwise not…

A bipartite producer-consumer network is constructed to describe the industrial structure. The edges from consumer to producer represent the choices of the consumer for the final products and the degree of producer can represent its market…

Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…

The power-law behavior is ubiquitous in a majority of real-world networks, and it was shown to have a strong effect on various combinatorial, structural, and dynamical properties of graphs. For example, it has been shown that in real-life…

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…

Two-sample network hypothesis testing is an important inference task with applications across diverse fields such as medicine, neuroscience, and sociology. Many of these testing methodologies operate under the implicit assumption that the…

Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have "unusual" properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the…

We investigate several geometric models of network which simultaneously have some nice global properties, that the small diameter property, the small-community phenomenon, which is defined to capture the common experience that (almost)…

In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution.

The friendship paradox in social networks states that your friends have more friends than you do, on average. Recently, a stronger variant of the paradox was shown to hold for most people within a network: `most of your friends have more…

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…

We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over Aug 1998 - Oct 2004. Specifically, we examine the distributions of (un)directed…

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…

Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…

The friendship paradox is the observation that the degrees of the neighbors of a node in any network will, on average, be greater than the degree of the node itself. In common parlance, your friends have more friends than you do. In this…

We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…

Power-law behaviors are common in many disciplines, especially in network science. Real-world networks, like disease spreading among people, are more likely to be interconnected communities, and show richer power-law behaviors than isolated…

Agents are represented by nodes on a random graph (e.g., small world or truncated power law). Each agent is endowed with a zero-mean random value that may be either positive or negative. All agents attempt to find relief, i.e., to reduce…