Related papers: Distinct Degrees and Their Distribution in Complex…
Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks.…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
We propose a network model with a fixed number of nodes and links with a dynamics which favors links between nodes differing in connectivity. Parameter regimes where the degree distributions follow power-laws, P(k) ~ k^-gamma, high…
The out-degree distribution of citation networks is investigated. Statistical data of the number of papers cited within a paper (out-degree) for different journals in the period 1991-1999 is reported. The out-degree distribution is…
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…
Despite great effort spent measuring topological features of large networks like the Internet, it was recently argued that sampling based on taking paths through the network (e.g., traceroutes) introduces a fundamental bias in the observed…
Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and…
In this article we discuss six degrees of separation, which has been proposed by Milgram, from a theoretical point of view. Simply if one has $k$ friends, the number $N$ of indirect friends goes up to $\sim k^d$ in $d$ degrees of…
Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally…
We investigate a network growth model in which the genealogy controls the evolution. In this model, a new node selects a random target node and links either to this target node, or to its parent, or to its grandparent, etc; all nodes from…
When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is…
We consider growing random networks $\{\mathcal G_n\}_{n \ge 1}$ where, at each time, a new vertex attaches itself to a collection of existing vertices via a fixed number $m \ge 1$ of edges, with probability proportional to an attachment…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
We propose a novel method for network inference from partially observed edges using a node-specific degree prior. The degree prior is derived from observed edges in the network to be inferred, and its hyper-parameters are determined by…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing…
Large-scale analysis of the distributions of the network graphs observed in naturally-occurring phenomena has revealed that the degrees of such graphs follow a power-law or lognormal distribution. Seshadhri, Pinar, and Kolda (J. ACM, 2013)…
Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…