Related papers: Recursive Formula for Labeled Graph Enumeration
This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, \Delta(k', k), describing specific degree-to- degree correlations is considered. The function is well suited to…
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real…
Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes.…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of…
Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product…
This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…
Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
Complex networks are relational data sets commonly represented as graphs. The analysis of their intricate structure is relevant to many areas of science and commerce, and data sets may reach sizes that require distributed storage and…
Finding frequently occurring subgraph patterns or network motifs in neural architectures is crucial for optimizing efficiency, accelerating design, and uncovering structural insights. However, as the subgraph size increases,…
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 apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature…