Related papers: General expression for the component size distribu…
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
We revisit the size distribution of finite components in infinite Configuration Model networks. We provide an elementary combinatorial proof about the sizes of birth-death trees which is more intuitive than previous proofs. We use this to…
Consider a critical random multigraph $\mathcal{G}_n$ with $n$ vertices constructed by the configuration model such that its vertex degrees are independent random variables with the same distribution $\nu$ (criticality means that the second…
We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We…
We consider the problems of computing the average degree and the size of a given network in a distributed fashion under quantized communication. We present two distributed algorithms which rely on quantized operation (i.e., nodes process…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…
This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution…
Identifying an optimal set of driver nodes to achieve synchronization via pinning control is a fundamental challenge in complex network science, limited by computational intractability and the lack of general theory. Here, leveraging a…
We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…
Connectivity is one of the most fundamental properties of wireless multi-hop networks. A network is said to be connected if there is a path between any pair of nodes. A convenient way to study the connectivity of a random network is by…
We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs. Graphs that are constrained by the joint…
We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…
We study the problem of the existence of a giant component in a random multipartite graph. We consider a random multipartite graph with $p$ parts generated according to a given degree sequence $n_i^{\mathbf{d}}(n)$ which denotes the number…