Search results for "Degree distribution"

2015

Protein-protein interaction (PPI) networks are associated with multiple types of biases partly rooted in technical limitations of the experimental techniques. Another source of bias are the different frequencies with which proteins have been studied for interaction partners. It is generally believed that proteins with a large number of interaction partners tend to be essential, evolutionarily conserved and involved in disease. It has been repeatedly reported that proteins driving tumor formation have a higher number of PPI partners. However, it has been noticed before that the degree distribution of PPI networks is biased towards disease proteins, which tend to have been studied more often …

Transience versus recurrence for scale-free spatial networks

2020

Weight-dependent random connection graphs are a class of local network models that combine scale-free degree distribution, small-world properties and clustering. In this paper we discuss recurrence or transience of these graphs, features that are relevant for the performance of search and information diffusion algorithms on the network.

Organization and evolution of synthetic idiotypic networks

2012

We introduce a class of weighted graphs whose properties are meant to mimic the topological features of idiotypic networks, namely the interaction networks involving the B-core of the immune system. Each node is endowed with a bit-string representing the idiotypic specificity of the corresponding B cell and a proper distance between any couple of bit-strings provides the coupling strength between the two nodes. We show that a biased distribution of the entries in bit-strings can yield fringes in the (weighted) degree distribution, small-worlds features, and scaling laws, in agreement with experimental findings. We also investigate the role of ageing, thought of as a progressive increase in …

The small-world of 'Le Petit Prince': Revisiting the word frequency distribution

2016

[EN] Many complex systems are naturally described through graph theory, and different kinds of systems described as networks present certain important characteristics in common. One of these features is the so-called scale-free distribution for its node s connectivity, which means that the degree distribution for the network s nodes follows a power law. Scale-free networks are usually referred to as small-world because the average distance between their nodes do not scale linearly with the size of the network, but logarithmically. Here we present a mathematical analysis on linguistics: the word frequency effect for different translations of the Le Petit Prince in different languages. Compar…

Feigenbaum graphs: a complex network perspective of chaos

2011

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map…

An Empirical Study of the Relation Between Community Structure and Transitivity

2012

One of the most prominent properties in real-world networks is the presence of a community structure, i.e. dense and loosely interconnected groups of nodes called communities. In an attempt to better understand this concept, we study the relationship between the strength of the community structure and the network transitivity (or clustering coefficient). Although intuitively appealing, this analysis was not performed before. We adopt an approach based on random models to empirically study how one property varies depending on the other. It turns out the transitivity increases with the community structure strength, and is also affected by the distribution of the community sizes. Furthermore, …

Horizontal visibility graphs: exact results for random time series

2009

The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables). After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We sh…

Collective Behavior of Price Changes of ERC-20 Tokens

2020

We analyze a network constructed from tokens developed on Ethereum platform. We collect a large data set of ERC-20 token prices; the total market capitalization of the token set is 50.2 billion (109) US dollars. The token set includes 541 tokens; each one of them has a market capitalization of 1 million US dollars or more. We construct and analyze the networks based on cross-correlation of tokens’ returns. We find that the degree distributions of the resulting graphs do not follow the power law degree distribution. We cannot find any hierarchical structures nor groupings of ERC-20 tokens in our analysis. peerReviewed

Social Networks and Labour–Education Market System

2015

Two facts about human beings are widely accepted: they are social creatures and they behave in a bounded rational way. In particular, this results in substantial use of social networks in individual decision-making. Before dealing with the issues of modelling individual behaviour in the labour–education market system, we have to recall some empirical facts known from the literature about this behaviour. This is exactly what this chapter provides.

The heterogeneity of inter-domain Internet application flows: entropic analysis and flow graph modelling

2013

The growing popularity of the Internet has triggered the proliferation of various applications, which possess diverse communication patterns and user behaviour. In this paper, the heterogeneous characteristics of Internet applications and traffic are investigated from a complex network and entropic perspective. On the basis of real-life flow data collected from a public network provided by an Internet service provider, flow graphs are constructed for five types of applications as follows: Web, P2P Download, P2P Stream, Video Stream and Instant Messaging. Three types of entropy measures are introduced to the flow graphs, and the heterogeneity of applications within a 24-h period is analysed …