Fast algorithm for successive computation of group betweenness centrality

Incorporation of spatial interactions in location networks to identify critical geo-referenced routes for assessing disease control measures on a large-scale campus

Respiratory diseases mainly spread through interpersonal contact. Class suspension is the most direct strategy to prevent the spread of disease through elementary or secondary schools by blocking the contact network. However, as university students usually attend courses in different buildings, the daily contact patterns on a university campus are complicated, and once disease clusters have occurred, suspending classes is far from an efficient strategy to control disease spread. The purpose of this study is to propose a methodological framework for generating campus location networks from a routine administration database, analyzing the community structure of the network, and identifying the critical links and nodes for blocking respiratory disease transmission. The data comes from the student enrollment records of a major comprehensive university in Taiwan. We combined the social network analysis and spatial interaction model to establish a geo-referenced community structure among the classroom buildings. We also identified the critical links among the communities that were acting as contact bridges and explored the changes in the location network after the sequential removal of the high-risk buildings. Instead of conducting a questionnaire survey, the study established a standard procedure for constructing a location network on a large-scale campus from a routine curriculum database. We also present how a location network structure at a campus could function to target the high-risk buildings as the bridges connecting communities for blocking disease transmission.

Implementation and Computation of a Value for Generalized Characteristic Function Games

Generalized characteristic function games are a variation of characteristic function games, in which the value of a coalition depends not only on the identities of its members, but also on the order in which the coalition is formed. This class of games is a useful abstraction for a number of realistic settings and economic situations, such as modeling relationships in social networks. To date, two main extensions of the Shapley value have been proposed for generalized characteristic function games: the Nowak-Radzik [1994] value and the Sánchez-Bergantiños [1997] value. In this context, the present article studies generalized characteristic function games from the point of view of implementation and computation. Specifically, the article makes two key contributions. First, building upon the mechanism by Dasgupta and Chiu [1998], we present a non-cooperative mechanism that implements both the Nowak-Radzik value and the Sánchez-Bergantiños value in Subgame-Perfect Nash Equilibria in expectations. Second, in order to facilitate an efficient computation supporting the implementation mechanism, we propose the Generalized Marginal-Contribution Nets representation for this type of game. This representation extends the results of Ieong and Shoham [2005] and Elkind et al. [2009] for characteristic function games and retains their attractive computational properties.

Range-limited centrality measures in complex networks

Here we present a range-limited approach to centrality measures in both nonweighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than ℓ=1,...,L in the case of nonweighted networks, and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than w(ℓ)=ℓΔ, ℓ=1,2...,L=R/Δ. These measures provide a systematic description on the positioning importance of a node (edge) with respect to its network neighborhoods one step out, two steps out, etc., up to and including the whole network. They are more informative than traditional centrality measures, as network transport typically happens on all length scales, from transport to nearest neighbors to the farthest reaches of the network. We show that range-limited centralities obey universal scaling laws for large nonweighted networks. As the computation of traditional centrality measures is costly, this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges, including the traditional ones. The scaling behavior can also be exploited to show that the ranking top list of nodes (edges) based on their range-limited centralities quickly freezes as a function of the range, and hence the diameter-range top list can be efficiently predicted. We also show how to estimate the typical largest node-to-node distance for a network of N nodes, exploiting the afore-mentioned scaling behavior. These observations were made on model networks and on a large social network inferred from cell-phone trace logs (∼5.5×10(6) nodes and ∼2.7×10(7) edges). Finally, we apply these concepts to efficiently detect the vulnerability backbone of a network (defined as the smallest percolating cluster of the highest betweenness nodes and edges) and illustrate the importance of weight-based centrality measures in weighted networks in detecting such backbones.

Fast computing betweenness centrality with virtual nodes on large sparse networks

Betweenness centrality is an essential index for analysis of complex networks. However, the calculation of betweenness centrality is quite time-consuming and the fastest known algorithm uses time and space for weighted networks, where and are the number of nodes and edges in the network, respectively. By inserting virtual nodes into the weighted edges and transforming the shortest path problem into a breadth-first search (BFS) problem, we propose an algorithm that can compute the betweenness centrality in time for integer-weighted networks, where is the average weight of edges and is the average degree in the network. Considerable time can be saved with the proposed algorithm when , indicating that it is suitable for lightly weighted large sparse networks. A similar concept of virtual node transformation can be used to calculate other shortest path based indices such as closeness centrality, graph centrality, stress centrality, and so on. Numerical simulations on various randomly generated networks reveal that it is feasible to use the proposed algorithm in large network analysis.

Graph analysis of epileptogenic networks in human partial epilepsy

PURPOSE

The current gold standard for the localization of the cortical regions responsible for the initiation and propagation of the ictal activity is through the use of invasive electrocorticography (ECoG). This method is utilized to guide surgical intervention in cases of medically intractable epilepsy by identifying the location and extent of the epileptogenic focus. Recent studies have proposed mechanisms in which the activity of epileptogenic cortical networks, rather than discrete focal sources, contributes to the generation of the ictal state. If true, selective modulation of key network components could be employed for the prevention and termination of the ictal state.

METHODS

Here, we have applied graph theory methods as a means to identify critical network nodes in cortical networks during both ictal and interictal states. ECoG recordings were obtained from a cohort of 25 patients undergoing presurgical monitoring for the treatment of intractable epilepsy at the Mayo Clinic (Rochester, MN, U.S.A.).

KEY FINDINGS

One graph measure, the betweenness centrality, was found to correlate with the location of the resected cortical regions in patients who were seizure-free following surgical intervention. Furthermore, these network interactions were also observed during random nonictal periods as well as during interictal spike activity. These network characteristics were found to be frequency dependent, with high frequency gamma band activity most closely correlated with improved postsurgical outcome as has been reported in previous literature.

SIGNIFICANCE

These findings could lead to improved understanding of epileptogenesis. In addition, this theoretically allows for more targeted therapeutic interventions through the selected modulation or disruption of these epileptogenic networks.