Related papers: Implementing Brouwer's database of strongly regula…
Given feasible strongly regular graph parameters $(v,k,\lambda,\mu)$ and a non-negative integer $d$, we determine upper and lower bounds on the order of a $d$-regular induced subgraph of any strongly regular graph with parameters…
We derive attainable upper bounds on the algebraic connectivity (spectral gap) of a regular graph in terms of its diameter and girth. This bound agrees with the well-known Alon-Boppana-Friedman bound for graphs of even diameter, but is an…
An approach to the enumeration of feasible parameters for strongly regular graphs is described, based on the pair of structural parameters (a,c) and the positive eigenvalue e. The Krein bound ensures that there are only finitely many…
In this paper, we derive nearly tight probabilistic norm bounds for a class of random matrices we call graph matrices. While the classical case of symmetric matrices with independent random entries (Wigner's matrices) is a special case, in…
In this paper we unify several existing regularity conditions for graphs, including strong regularity, $k$-isoregularity, and the $t$-vertex condition. We develop an algebraic composition/decomposition theory of regularity conditions. Using…
We derive a new upper bound on the algebraic connectivity of a regular graph using the Higman-Sims technique. Together with a new result on the connectivity of the neighbourhood graph of strongly regular graphs, our result gives a…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
The vast amounts of data used in social, business or traffic networks, biology and other natural sciences are often managed in graph-based data sets, consisting of a few thousand up to billions and trillions of vertices and edges,…
Graph databases have been the subject of significant research and development. Problems such as modularity, centrality, alignment, and clustering have been formalized and solved in various application contexts. In this paper, we focus on…
This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\bf [On the sum of k largest…
This paper studies the discovery of approximate rules in property graphs. We propose a semantically meaningful measure of error for mining graph entity dependencies (GEDs) at almost hold, to tolerate errors and inconsistencies that exist in…
A canonical problem in graph mining is the detection of dense communities. This problem is exacerbated for a graph with a large order and size -- the number of vertices and edges -- as many community detection algorithms scale poorly. In…
We propose a novel unsupervised approach for linking records across arbitrarily many files, while simultaneously detecting duplicate records within files. Our key innovation is to represent the pattern of links between records as a {\em…
We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually…
With the proliferation of large irregular sparse relational datasets, new storage and analysis platforms have arisen to fill gaps in performance and capability left by conventional approaches built on traditional database technologies and…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…
Sequences of group interactions, such as emails, online discussions, and co-authorships, are ubiquitous; and they are naturally represented as a stream of hyperedges. Despite their broad potential applications, anomaly detection in…
Given a massive graph, how can we exploit its hierarchical structure for concisely but exactly summarizing the graph? By exploiting the structure, can we achieve better compression rates than state-of-the-art graph summarization methods?…
In many real world networks, a vertex is usually associated with a transaction database that comprehensively describes the behaviour of the vertex. A typical example is the social network, where the behaviour of every user is depicted by a…
Recent advances in computational methods for intractable models have made network data increasingly amenable to statistical analysis. Exponential random graph models (ERGMs) emerged as one of the main families of models capable of capturing…