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The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…
In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…
The assortative behavior of a network is the tendency of similar (or dissimilar) nodes to connect to each other. This tendency can have an influence on various properties of the network, such as its robustness or the dynamics of spreading…
We introduce a new approach to constructing networks with realistic features. Our method, in spite of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of network types with prescribed…
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in- and out-degrees. As the number of…
We describe a procedure that allows continuously tuning the average degree $\langle k \rangle$ of uncorrelated networks with power-law degree distribution $p(k)$. Inn order to do this, we modify the low-$k$ region of $p(k)$, while…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
We propose algorithms for construction and random generation of hypergraphs without loops and with prescribed degree and dimension sequences. The objective is to provide a starting point for as well as an alternative to Markov chain Monte…
Degree-based graph construction is an ubiquitous problem in network modeling, ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive…
In complex networks it is common to model a network or generate a surrogate network based on the conservation of the network's degree distribution. We provide an alternative network model based on the conservation of connection density…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$,…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
We evaluate analytically and numerically the size of the frozen core and various scaling laws for critical Boolean networks that have a power-law in- and/or out-degree distribution. To this purpose, we generalize an efficient method that…
We study the capability to learn and to generate long-range, power-law correlated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a sequence. We…
There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…
We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…