Related papers: Degree-based graph construction

The construction of large-scale, low-latency networks becomes difficult as the number of nodes increases. In general, the way to construct a theoretically optimal solution is unknown. However, it is known that some methods can construct…

A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…

A finite non-increasing sequence of positive integers $d = (d_1\geq \cdots\geq d_n)$ is called a degree sequence if there is a graph $G = (V,E)$ with $V = \{v_1,\ldots,v_n\}$ and $deg(v_i)=d_i$ for $i=1,\ldots,n$. In that case we say that…

Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…

There are a variety of existing conditions for a degree sequence to be graphic. When a degree sequence satisfies any of these conditions, there exists a graph that realizes the sequence. We formulate several novel sufficient graphicality…

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…

In a directed graph, the imbalance of a vertex is its outdegree minus its indegree. We characterize the sequences that are realizable as the sequence of imbalances of a simple directed graph. Moreover, a realization of a realizable sequence…

We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…

Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…

For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The…

We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…

In order to support the real-time interaction with LLMs and the instant search or the instant recommendation on social media, it becomes an imminent problem to build a k-NN graph or an indexing graph for the massive number of vectorized…

Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…

Drug Discovery is a fundamental and ever-evolving field of research. The design of new candidate molecules requires large amounts of time and money, and computational methods are being increasingly employed to cut these costs. Machine…

We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…

In this paper we consider module-composed graphs, i.e. graphs which can be defined by a sequence of one-vertex insertions v_1,...,v_n, such that the neighbourhood of vertex v_i, 2<= i<= n, forms a module (a homogeneous set) of the graph…

We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the…

We give the first analysis of the computational complexity of {\it coalition structure generation over graphs}. Given an undirected graph $G=(N,E)$ and a valuation function $v:2^N\rightarrow\RR$ over the subsets of nodes, the problem is to…

There are typically several nonisomorphic graphs having a given degree sequence, and for any two degree sequence terms it is often possible to find a realization in which the corresponding vertices are adjacent and one in which they are…

We study the random graph G_{n,\lambda/n} conditioned on the event that all vertex degrees lie in some given subset S of the non-negative integers. Subject to a certain hypothesis on S, the empirical distribution of the vertex degrees is…