Related papers: Asymptotic Normality for the Size of Graph Tries b…

The topic is the average order of a connected induced subgraph of a graph. This generalizes, to graphs in general, the average order of a subtree of a tree. In 1984, Jamison proved that the average order, over all trees of order $n$, is…

Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…

This paper introduces a novel graph-analytic approach for detecting anomalies in network flow data called GraphPrints. Building on foundational network-mining techniques, our method represents time slices of traffic as a graph, then counts…

Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…

We study the $k$-core of a random (multi)graph on $n$ vertices with a given degree sequence. In our previous paper [Random Structures Algorithms 30 (2007) 50--62] we used properties of empirical distributions of independent random variables…

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…

How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…

A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…

Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures,…

We study maximal clades in random phylogenetic trees with the Yule-Harding model or, equivalently, in binary search trees. We use probabilistic methods to reprove and extend earlier results on moment asymptotics and asymptotic normality. In…

Consider a family $\mathcal{T}$ of 3-connected graphs of moderate growth, and let $\mathcal{G}$ be the class of graphs whose 3-connected components are graphs in $\mathcal{T}$. We present a general framework for analyzing such graphs…

Graph classification, which aims to identify the category labels of graphs, plays a significant role in drug classification, toxicity detection, protein analysis etc. However, the limitation of scale in the benchmark datasets makes it easy…

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 consider the asymptotic normalcy of families of random variables $X$ which count the number of occupied sites in some large set. We write $Prob(X=m)=p_mz_0^m/P(z_0)$, where $P(z)$ is the generating function $P(z)=\sum_{j=0}^{N}p_jz^j$…

In recent years, researchers proposed several algorithms that compute metric quantities of real-world complex networks, and that are very efficient in practice, although there is no worst-case guarantee. In this work, we propose an…

Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…

Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…

In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…

We confirm a conjecture by Everett, Sinclair, and Dankelmann~[Some Centrality results new and old, J. Math. Sociology 28 (2004), 215--227] regarding the problem of maximizing closeness centralization in two-mode data, where the number of…

Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…