Related papers: The entropy of network ensembles

The structure of a network is an unlabeled graph, yet graphs in most models of complex networks are labeled by meaningless random integers. Is the associated labeling noise always negligible, or can it overpower the network-structural…

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…

We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…

Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…

Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…

Ensembles of networks are used as null-models to discriminate network structures. We present an efficient algorithm, based on the maximal entropy method to generate network ensembles defined by the degree sequence and the rich-club…

A vast variety of biological, social, and economical networks shows topologies drastically differing from random graphs; yet the quantitative characterization remains unsatisfactory from a conceptual point of view. Motivated from the…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…

We describe an ensemble of growing scale-free networks in an equilibrium framework, providing insight into why the exponent of empirical scale-free networks in nature is typically robust. In an analogy to thermostatistics, to describe the…

A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…

Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…

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…

It is often claimed that the entropy of a network's degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former…

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…

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…

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…

We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a…

Large-scale human social network structure is typically inferred from digital trace samples of online social media platforms or mobile communication data. Instead, here we investigate the social network structure of a complete population,…

We discover a first-order phase transition in the canonical ensemble of random unlabeled networks with a prescribed average number of links. The transition is caused by the nonconcavity of microcanonical entropy. Above the critical point…

We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…