Related papers: Centrality scaling in large networks

Closeness centrality, first considered by Bavelas (1948), is an importance measure of a node in a network which is based on the distances from the node to all other nodes. The classic definition, proposed by Bavelas (1950), Beauchamp…

All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…

Who is more important in a network? Who controls the flow between the nodes or whose contribution is significant for connections? Centrality metrics play an important role while answering these questions. The betweenness metric is useful…

Hierarchy and centrality are two popular notions used to characterize the importance of entities in complex systems. Indeed, many complex systems exhibit a natural hierarchical structure, and centrality is a fundamental characteristic…

A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [Bonacich, 2001], measures the number of attenuated paths that exist between nodes. We introduce a normalized…

In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…

We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…

We demonstrate that the distribution of betweenness centrality (BC), a global structural metric based on network flow, is an invariant quantity in most planar graphs. We confirm this invariance through an empirical analysis of street…

The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…

The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact…

Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to…

We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…

An important source of high clustering coefficient in real-world networks is transitivity. However, existing approaches for modeling transitivity suffer from at least one of the following problems: i) they produce graphs from a specific…

Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability. Several centrality measures have been proposed recently to evaluate the performance of nodes based on their…

Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…

Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…

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…

Centrality is a fundamental concept in network science, providing critical insights into the structure and dynamics of complex systems such as social, transportation, biological and financial networks. Despite its extensive use, there is no…

Many real world systems can be expressed as complex networks of interconnected nodes. It is frequently important to be able to quantify the relative importance of the various nodes in the network, a task accomplished by defining some…