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The complexity of a graph can be obtained as a derivative of a variation of the zeta function or a partial derivative of its generalized characteristic polynomial evaluated at a point [\textit{J. Combin. Theory Ser. B}, 74 (1998), pp.…
Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that…
Eigenvalues of a graph are of high interest in graph analytics for Big Data due to their relevance to many important properties of the graph including network resilience, community detection and the speed of viral propagation. Accurate…
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…
We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality…
Sparse exchangeable graphs on $\mathbb{R}_+$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as…
In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple…
Random samples are lossy summaries which allow queries posed over the data to be approximated by applying an appropriate estimator to the sample. The effectiveness of sampling, however, hinges on estimator selection. The choice of…
Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected.…
Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…
We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
In image generation, generative models can be evaluated naturally by visually inspecting model outputs. However, this is not always the case for graph generative models (GGMs), making their evaluation challenging. Currently, the standard…