Related papers: Double Clustering and Graph Navigability
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…
A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
The graph reconstruction conjecture states that all graphs on at least three vertices are determined up to isomorphism by their deck. In this paper, a general framework for this problem is proposed to simply explain the reconstruction of…
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions…
We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
Bidirected graphs are a common generalisation of directed graphs where arcs can also be incoming to both their incident nodes, or outgoing from both their incident nodes. Such arcs allow a walk to change direction. Some algorithms can…
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…
Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…
We consider the problem of searching for a node on a labelled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…
A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…
Alternative paths in a network play an important role in its functionality as they can maintain the information flow under node/link failures. In this paper we explore the navigation of a network taking into account the alternative paths…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…