Related papers: Recursive Formula for Labeled Graph Enumeration
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
Motivated by the question of how macromolecules assemble, the notion of an {\it assembly tree} of a graph is introduced. Given a graph $G$, the paper is concerned with enumerating the number of assembly trees of $G$, a problem that applies…
Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
We continue the line of research on graph compression started with WebGraph, but we move our focus to the compression of social networks in a proper sense (e.g., LiveJournal): the approaches that have been used for a long time to compress…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons to describe large and unlabelled networks are…
Similarity metrics are central in the theory of large networks and graph limits. For bounded-degree graphs, the Benjamini--Schramm metric records the distribution of rooted neighbourhoods, while the stronger colored-neighbourhood metric…
A model algorithm is proposed to study subsequent partitions of complex networks describing social structures. The partitions are supposed to appear as actions of rivaling leaders corresponding to nodes with large degrees. The condition of…
Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
Feedforward multilayer networks trained by supervised learning have recently demonstrated state of the art performance on image labeling problems such as boundary prediction and scene parsing. As even very low error rates can limit…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
We tackle the problem of inferring node labels in a partially labeled graph where each node in the graph has multiple label types and each label type has a large number of possible labels. Our primary example, and the focus of this paper,…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
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…
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…