Related papers: Convexity in scientific collaboration networks
A convex network can be defined as a network such that every connected induced subgraph includes all the shortest paths between its nodes. Fully convex network would therefore be a collection of cliques stitched together in a tree. In this…
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…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
In this work, we introduce a new graph convexity, that we call Cycle Convexity, motivated by related notions in Knot Theory. For a graph $G=(V,E)$, define the interval function in the Cycle Convexity as $I_{cc}(S) = S\cup \{v\in V(G)\mid…
The primary objective of this paper is to investigate the notions of geometric and sequential convexity within a graph-theoretic framework, with the aim of examining various structural properties and exploring the connection between these…
Convexity is a notion that has been defined for subsets of $\RR^n$ and for subsets of general graphs. A convex cut of a graph $G=(V, E)$ is a $2$-partition $V_1 \dot{\cup} V_2=V$ such that both $V_1$ and $V_2$ are convex, \ie shortest paths…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large…
The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices. A complete…
Centrality measures aim to indicate who is important in a network. Various notions of `being important' give rise to different centrality measures. In this paper, we study how important the central vertices are for the connectivity…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Several studies exist which use scientific literature for comparing scientific activities (e.g., productivity, and collaboration). In this study, using co-authorship data over the last 40 years, we present the evolutionary dynamics of multi…
Given an undirected graph $G = (V,E)$, the cut polytope $\mathrm{CUT}(G)$ is defined as the convex hull of the incidence vectors of all cuts in $G$. The 1-skeleton of $\mathrm{CUT}(G)$ is a graph whose vertex set is the vertex set of the…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…
A large body of work has been devoted to defining and identifying clusters or communities in social and information networks. We explore from a novel perspective several questions related to identifying meaningful communities in large…