Related papers: Enumerating ODE Equivalent Homogeneous Networks
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
We extend some results on even sets of nodes which have been proved for surfaces up to degree 6 to surfaces up to degree 10. In particular, we give a formula for the minimal cardinality of a nonempty even set of nodes.
Song, Havlin and Makse (2005) have recently used a version of the box-counting method, called the node-covering method, to quantify the self-similar properties of 43 cellular networks: the minimal number $N_V$ of boxes of size $\ell$ needed…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
In many causal learning problems, variables of interest are often not all measured over the same observations, but are instead distributed across multiple datasets with overlapping variables. Tillman et al. (2008) presented the first…
We consider a heterogeneous network with mobile edge computing, where a user can offload its computation to one among multiple servers. In particular, we minimize the system-wide computation overhead by jointly optimizing the individual…
Edge-connectivity is a classic measure for reliability of a network in the presence of edge failures. $k$-restricted edge-connectivity is one of the refined indicators for fault tolerance of large networks. Matching preclusion and…
For models whose evolution takes place on a network it is often necessary to augment the mean-field approach by considering explicitly the degree dependence of average quantities (heterogeneous mean-field). Here we introduce the degree…
Biological cells are built up from many different constituents of varying size and stiffness which all contribute to the cell's mechanical properties. Despite this heterogeneity, in the analysis of experimental measurements such as atomic…
Let $H$ and $G$ be graphs such that $H$ has at least 3 vertices and is connected. The $H$-line graph of $G$, denoted by $HL(G)$, is that graph whose vertices are the edges of $G$ and where two vertices of $HL(G)$ are adjacent if they are…
A hypergraph is a data structure composed of nodes and hyperedges, where each hyperedge is an any-sized subset of nodes. Due to the flexibility in hyperedge size, hypergraphs represent group interactions (e.g., co-authorship by more than…
Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to…
A graph property is monotone if it is closed under removal of vertices and edges. In this paper we consider the following edge-deletion problem; given a monotone property P and a graph G, compute the smallest number of edge deletions that…
Fr\"oberg's classical theorem about edge ideals with $2$-linear resolution can be regarded as a classification of graphs whose edge ideals have linearity defect zero. Extending his theorem, we classify all graphs whose edge ideals have…
We conduct a systematic study of asynchronous models of distributed computing consisting of identical finite-state devices that cooperate in a network to decide if the network satisfies a given graph-theoretical property. Models discussed…
Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the…
A simplicial polytope is a polytope with all its facets being combinatorially equivalent to simplices. We deal with the edge connectivity of the graphs of simplicial polytopes. We first establish that, for any $d\ge 3$, for any $d\ge 3$,…
A coupled cell network is a model for many situations such as food webs in ecosystems, cellular metabolism, economical networks... It consists in a directed graph $G$, each node (or cell) representing an agent of the network and each…
We consider a general heterogeneous network in which, besides general propagation effects (shadowing and/or fading), individual base stations can have different emitting powers and be subject to different parameters of Hata-like path-loss…
We propose a similarity-based method, using the similarity between nodes, to address the problem of classification in partially labeled networks. The basic assumption is that two nodes are more likely to be categorized into the same class…