Related papers: The Irreducible Spine(s) of Undirected Networks

Networks provide an informative, yet non-redundant description of complex systems only if links represent truly dyadic relationships that cannot be directly traced back to node-specific properties such as size, importance, or coordinates in…

In a finite undirected simple graph, a {\it chordless cycle} is an induced subgraph which is a cycle. We propose two algorithms to enumerate all chordless cycles of such a graph. Compared to other similar algorithms, the proposed algorithms…

In this paper, we employ the decomposition of a directed network as an undirected graph plus its associated node metadata to characterise the cyclic structure found in directed networks by finding a Minimal Cycle Basis of the undirected…

A cycle basis in an undirected graph is a minimal set of simple cycles whose symmetric differences include all Eulerian subgraphs of the given graph. We define a rooted cycle basis to be a cycle basis in which all cycles contain a specified…

In a finite undirected simple graph, a chordless cycle is an induced subgraph which is a cycle. A graph is called cyclically orientable if it admits an orientation in which every chordless cycle is cyclically oriented. We propose an…

This paper studies the controllability backbone problem in dynamical networks defined over graphs. The main idea of the controllability backbone is to identify a small subset of edges in a given network such that any subnetwork containing…

We consider intrinsic linking and knotting in the context of directed graphs. We construct an example of a directed graph that contains a consistently oriented knotted cycle in every embedding. We also construct examples of intrinsically…

The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…

Recent advances in the field of network embedding have shown that low-dimensional network representation is playing a critical role in network analysis. Most existing network embedding methods encode the local proximity of a node, such as…

A graph embedded in the 3-sphere is called irreducible if it is non-splittable and for any 2-sphere embedded in the 3-sphere that intersects the graph at one point the graph is contained in one of the 3-balls bounded by the 2-sphere. We…

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…

The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…

For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…

Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…

Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…

Attributed network embedding aims to learn low-dimensional vector representations for nodes in a network, where each node contains rich attributes/features describing node content. Because network topology structure and node attributes…

We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We…

In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…

In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary…

We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph is intrinsically linked, namely every spatial embedding of…