Properties Of Real Networks Research Articles

Strong connectivity in real directed networks

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behavior of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering-a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes and confirm our results on many real-world networks, including ecological, neural, trade, and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. This means that many dynamical processes on networks can depend significantly on a small fraction of edges.

Two Kinds of Laplacian Spectra and Degree Kirchhoff Index of the Weighted Corona Networks

Recently, the study related to network has aroused wide attention of the scientific community. Many problems can be usefully represented by corona graphs or networks. Meanwhile, the weight is a vital factor in characterizing some properties of real networks. In this paper, we give complete information about the signless Laplacian spectra of the weighted corona of a graph G1 and a regular graph G2 and the complete information about the normalized Laplacian spectra of the weighted corona of two regular graphs. The corresponding linearly independent eigenvectors of all these eigenvalues are also obtained. The spanning trees’ total number and the degree Kirchhoff index of the weighted corona graph are computed.

Average path length and degree distribution of networks generated by random sequence

Considering that many real networks do not have strict self-similarity property, compared with deterministic evolutionary fractal networks, networks with random sequence structure may be more in accordance with the properties of real networks. In this paper, we generate a hierarchical network by a random sequence based on BRV model. Using the encoding method, we present a way to judge whether two nodes are neighbors and calculate the total path length of the network. We get the degree distribution and limit formula of the average path length of a class of networks, which are obtained by analytical method and iterative calculation.

Топология сети межбанковского кредитования в агентной модели банковской системы

The study analyzes the topology of the interbank network in the agent-based model of the banking system with detailed description of the protocols and stylized one of the external (with respect to the banking system) economy. It is shown that the main incentive for the inter­bank market creation originates from liquidity gaps resulting from maturities mismatch bet­ween deposits and credits. The impact of this effect on the dynamics of total capital and cash in the case of increasing term structure of the yield curve generating credit and deposit’s maturities mismatch as a result of banks optimizing behavior, is illustrated. Different properties of this graph are compared to those of the real interbank networks. It is shown that the model in which banks are represented by agents-automata can reproduce various topological properties of the real interbank networks. These properties are: significant size of the giant strongly connected component, fat‑tailed nature of the distributions of In- and Out-degrees, fat-tailed nature of the distribution of allocated funds, disassortativity, nonuniformity of the distribution of clustering coefficient over the vertices. The properties which can be reproduced only in the model with a more detailed description of agents’ behavior were also marked out. These properties are the following: absence of the oriented cycles in the networks with low aggregation of the data, low fraction of the banks not participating in the interbank market and of the net-creditor banks, absence of fat tails in the distribution over the borrowed funds, low clustering coefficient. The reasons for such a difference between the properties of model networks and the real ones are noted. The changes of the model needed to reproduce such properties of real networks are discussed.

Exponential random graph models for networks with community structure

Although the community structure organization is an important characteristic of real-world networks, most of the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both the classical blockmodel and its degree-corrected counterpart and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field.

A scale-free graph model based on bipartite graphs

Most biological networks have some common properties, on which models have to fit. The main one is that those networks are scale-free, that is that the distribution of the vertex degrees follows a power-law. Among the existing models, the ones which fit those characteristics best are based on a time evolution which makes impossible the analytic calculation of the number of motifs in the network. Focusing on applications, this calculation is very important to decompose networks in a modular manner, as proposed by Milo et al.. On the contrary, models whose construction does not depend on time, miss one or several properties of real networks or are not computationally tractable. In this paper, we propose a new random graph model that satisfies the global features of biological networks and the non-time-dependency condition. It is based on a bipartite graph structure, which has a biological interpretation in metabolic networks.

PROPERTIES OF AN EVOLVING DIRECTED NETWORK WITH LOCAL RULES AND INTRINSIC VARIABLES

We present a simple model of an evolving directed network based on local rules. It leads to a complex network with the properties of real systems, like scale-free distribution of outgoing and incoming connectivity, and a hierarchical structure. Each node is characterised by an intrinsic variable S, and the number of outgoing links k out . As a result of network evolution the number of nodes and links (as well as their location) changes in time. For critical values of control parameters there is a transition to a scale-free network. Results for connectivity distribution found analytically agree with numerical calculations. Our model also reproduces other nontrivial properties of real networks, e.g. a large clustering coefficient and weak correlations between the age of a node and its connectivity. We have discovered an unexpected phenomenon that noise can increase the value of the clustering coefficient, whose large value is characteristic for a regular network.