Related papers: Modulus on graphs as a generalization of standard …
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
This note summarizes the state of what is known about the tractability of the problem ModPath, which asks if an input undirected graph contains a simple st-path whose length satisfies modulo constraints. We also consider the problem…
We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…
This paper develops a fundamental theory of realizations of linear and group codes on general graphs using elementary group theory, including basic group duality theory. Principal new and extended results include: normal realization…
Let $R$ be a commutative ring with identity and $G$ a graph. An extending generalized spline on $G$ is a vertex labeling $f \in \prod_{v} M_v$, where for each edge $e=uv$ there exists an $R$-module $M_{uv}$ together with homomorphisms $…
The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of order $n$ whose metric subgraphs are all paths if and only…
Let $r\geq 3$ be an integer and $G$ be a graph. Let $\delta(G), \Delta(G)$, $\alpha(G)$ and $\mu(G)$ denotes minimum degree, maximum degree, independence number and matching number of $G$, respectively. Recently, Caro, Davila and Pepper…
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
We study diffusion (random walks) on recursive scale-free graphs, and contrast the results to similar studies in other analytically soluble media. This allows us to identify ways in which diffusion in scale-free graphs is special. Most…
The walk distances in graphs are defined as the result of appropriate transformations of the $\sum_{k=0}^\infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a connected weighted graph and $t$ is a sufficiently…
We introduce the notion of watching systems in graphs, which is a generalization of that of identifying codes. We give some basic properties of watching systems, an upper bound on the minimum size of a watching system, and results on the…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
We show that the multi-commodity max-flow/min-cut gap for series-parallel graphs can be as bad as 2, matching a recent upper bound Chakrabarti, Jaffe, Lee, and Vincent for this class, and resolving one side of a conjecture of Gupta, Newman,…
In this paper, we extend the sampling theory on graphs by constructing a framework that exploits the structure in product graphs for efficient sampling and recovery of bandlimited graph signals that lie on them. Product graphs are graphs…
This note is but a research announcement, summarizing and explaining results proven and detailed in forthcoming papers. When one studies families of objects over curves, and the objects are parametrized by a Deligne-Mumford stack M, then…
In this note we study and compare three graph invariants related to the 'compactness' of graph drawing in the plane: the dilation coefficient, defined as the smallest possible quotient between the longest and the shortest edge length; the…
With the recent rise in the amount of structured data available, there has been considerable interest in methods for machine learning with graphs. Many of these approaches have been kernel methods, which focus on measuring the similarity…
The traditional complex network approach considers only the shortest paths from one node to another, not taking into account several other possible paths. This limitation is significant, for example, in urban mobility studies. In this short…
The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…