Related papers: Assortativity in random line graphs
We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
Many naturally occurring networks have a power-law degree distribution as well as a non-zero degree correlation. Despite this, most studies analyzing the robustness to random node-deletion and vulnerability to targeted node-deletion have…
Extending previous results in the literature, random colored substitution networks and degree dimension are defined in this paper. The scale-freeness of these networks is proved by introducing a new definition for degree dimension that is…
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…
We perform an analytical analysis of the long-range degree correlation of the giant component in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the…
In a highly influential paper twenty years ago, Barab\'asi and Albert [Science 286, 509 (1999)] showed that networks undergoing generic growth processes with preferential attachment evolve towards scale-free structures. In any finite…
We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdos-Renyi random graphs, vertex random graphs are generalizations of geometric random graphs, and…
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the…
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the…
This Master's thesis examines the properties of large degree vertices in random recursive directed acyclic graphs (RRDAGs), a generalization of the well-studied random recursive tree (RRT) model. Using a novel adaptation of Kingman's…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
Scale-free networks are a recently developed approach to model the interactions found in complex natural and man-made systems. Such networks exhibit a power-law distribution of node link (degree) frequencies n(k) in which a small number of…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…