Related papers: Convex Graph Invariants
Convexity in a network (graph) has been recently defined as a property of each of its subgraphs to include all shortest paths between the nodes of that subgraph. It can be measured on the scale [0, 1] with 1 being assigned to fully convex…
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
The work in this thesis concerns the investigation of eigenvalues of the Laplacian matrix, normalized Laplacian matrix, signless Laplacian matrix and distance signless Laplacian matrix of graphs. In Chapter 1, we present a brief…
Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with…
In 2017, Nikiforov introduced the concept of the $A_{\alpha}$-matrix, as a linear convex combination of the adjacency matrix and the degree diagonal matrix of a graph. This matrix has attracted increasing attention in recent years, as it…
Directed acyclic graphs whose nodes are all the divisors of a positive integer $n$ and arcs $(a,b)$ defined by $a$ divides $b$ are considered. Fourteen graph invariants such as order, size, and the number of paths are investigated for two…
Graphs are quickly emerging as a leading abstraction for the representation of data. One important application domain originates from an emerging discipline called "connectomics". Connectomics studies the brain as a graph; vertices…
Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
We introduce a persistence-type invariant for finite weighted graphs based on combinatorial multivector dynamics. For each threshold parameter, a relation matrix determines a graph multivector field, whose induced directed dynamics admits a…
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.
Let $G$ be a graph, and let $\lambda(G)$ denote the smallest eigenvalue of $G$. First, we provide an upper bound for $\lambda(G)$ based on induced bipartite subgraphs of $G$. Consequently, we extract two other upper bounds, one relying on…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
Functionality ($\mathrm{fun}$) is a graph parameter that generalizes graph degeneracy defined by Alecu et al. [JCTB, 2021]. They research the relation of functionality to many other graphs parameters (tree-width, clique-width, VC-dimension,…
We consider a hierarchy of graph invariants that naturally extends the spectral invariants defined by F\"urer (Lin. Alg. Appl. 2010) based on the angles formed by the set of standard basis vectors and their projections onto eigenspaces of…