Related papers: Greedy Connectivity of Geographically Embedded Gra…
This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…
In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], the authors proposed a simple measure for network robustness under malicious attacks on nodes. With a greedy algorithm, they found the optimal structure with respect to this…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…
Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property,…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which…
In this work, we propose a large-graph limit estimate of the matching coverage for several matching algorithms, on general graphs generated by the configuration model. For a wide class of {\em local} matching algorithms, namely, algorithms…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as…
The analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be…
This article discusses random hypergraphs with varying hyperedge sizes, admitting large hyperedges with size tending to infinity, and heavy-tailed limiting hyperedge size distributions. The main result describes a threshold for the random…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
Searching for optimal ways in a network is an important task in multiple application areas such as social networks, co-citation graphs or road networks. In the majority of applications, each edge in a network is associated with a certain…
Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the…
Random scale-free networks are ultrasmall worlds. The average length of the shortest paths in networks of size N scales as lnlnN. Here we show that these ultrasmall worlds can be navigated in ultrashort time. Greedy routing on scale-free…