An official website of the United States government
Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend this notion to a group of vertices in a weighted graph, and then study the problem of finding a subset S of k vertices to maximize its CFCC C(S), both theoretically and experimentally. We show that the problem is NP-hard, but propose two greedy algorithms for minimizing the reciprocal of C(S) with provable guarantees using the monotoncity and supermodularity. The first is a deterministic algorithm with an approximation factor (1−kk−1⋅1e) and cubic running time; while the second is a randomized algorithm with a (1−kk−1⋅1e−ϵ)-approximation and nearly-linear running time for any ϵ>0. Extensive experiments on model and real networks demonstrate that our algorithms are effective and efficient, with the second algorithm being scalable to massive networks with more than a million vertices.
more »
« less
Sensitivity and Reliability in Incomplete Networks: Centrality Metrics to Community Scoring Functions
In this paper we evaluate the effect of noise on community scoring and centrality-based parameters with respect to two different aspects of network analysis: (i) sensitivity, that is how the parameter value changes as edges are removed and (ii) reliability in the context of message spreading, that is how the time taken to broadcast a message changes as edges are removed. Our experiments on synthetic and real-world networks and three different noise models demonstrate that for both the aspects over all networks and all noise models, permanence qualifies as the most effective metric. For the sensitivity experiments closeness centrality is a close second. For the message spreading experiments, closeness and betweenness centrality based initiator selection closely competes with permanence. This is because permanence has a dual characteristic where the cumulative permanence over all vertices is sensitive to noise but the ids of the top-rank vertices, which are used to find seeds during message spreading remain relatively stable under noise.
more »
« less
- Award ID(s):
- 1533881
- PAR ID:
- 10017954
- Date Published:
- Journal Name:
- The 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This paper describes a group-level classification of 14 patients with prefrontal cortex (pFC) lesions from 20 healthy controls using multi-layer graph convolutional networks (GCN) with features inferred from the scalp EEG recorded from the encoding phase of working memory (WM) trials. We first construct undirected and directed graphs to represent the WM encoding for each trial for each subject using distance correlation- based functional connectivity measures and differential directed information-based effective connectivity measures, respectively. Centrality measures of betweenness centrality, eigenvector centrality, and closeness centrality are inferred for each of the 64 channels from the brain connectivity. Along with the three centrality measures, each graph uses the relative band powers in the five frequency bands - delta, theta, alpha, beta, and gamma- as node features. The summarized graph representation is learned using two layers of GCN followed by mean pooling, and fully connected layers are used for classification. The final class label for a subject is decided using majority voting based on the results from all the subject's trials. The GCN-based model can correctly classify 28 of the 34 subjects (82.35% accuracy) with undirected edges represented by functional connectivity measure of distance correlation and classify all 34 subjects (100% accuracy) with directed edges characterized by effective connectivity measure of differential directed information.more » « less
-
The combinatorial problem in this paper is motivated by a variant of the famous traveling salesman problem where the salesman must return to the starting point after each delivery. The total length of a delivery route is related to a metric known as closeness centrality. The closeness centrality of a vertex v in a graph G was defined in 1950 by Bavelas to be CC(v)=|V(G)|−1SD(v), where SD(v) is the sum of the distances from v to each of the other vertices (which is one-half of the total distance in the delivery route). We provide a real-world example involving the Metro Atlanta Rapid Transit Authority rail network and identify stations whose SD values are nearly identical, meaning they have a similar proximity to other stations in the network. We then consider theoretical aspects involving asymmetric trees. For integer values of k, we considered the asymmetric tree with paths of lengths k,2k,…,nk that are incident to a center vertex. We investigated trees with different values of k, and for k=1 and k=2, we established necessary and sufficient conditions for the existence of two vertices with identical SD values, which has a surprising connection to the triangular numbers. Additionally, we investigated asymmetric trees with paths incident to two vertices and found a sufficient condition for vertices to have equal SD values. This leads to new combinatorial proofs of identities arising from Pascal’s triangle.more » « less
-
null (Ed.)Abstract This paper introduces the notions of chained and semi-chained graphs. The chain of a graph, when existent, refines the notion of bipartivity and conveys important structural information. Also the notion of a center vertex $$v_c$$ v c is introduced. It is a vertex, whose sum of p powers of distances to all other vertices in the graph is minimal, where the distance between a pair of vertices $$\{v_c,v\}$$ { v c , v } is measured by the minimal number of edges that have to be traversed to go from $$v_c$$ v c to v . This concept extends the definition of closeness centrality. Applications in which the center node is important include information transmission and city planning. Algorithms for the identification of approximate central nodes are provided and computed examples are presented.more » « less
-
Abstract We define a bridge node to be a node whose neighbor nodes are sparsely connected to each other and are likely to be part of different components if the node is removed from the network. We propose a computationally light neighborhood-based bridge node centrality (NBNC) tuple that could be used to identify the bridge nodes of a network as well as rank the nodes in a network on the basis of their topological position to function as bridge nodes. The NBNC tuple for a node is asynchronously computed on the basis of the neighborhood graph of the node that comprises of the neighbors of the node as vertices and the links connecting the neighbors as edges. The NBNC tuple for a node has three entries: the number of components in the neighborhood graph of the node, the algebraic connectivity ratio of the neighborhood graph of the node and the number of neighbors of the node. We analyze a suite of 60 complex real-world networks and evaluate the computational lightness, effectiveness, efficiency/accuracy and uniqueness of the NBNC tuple vis-a-vis the existing bridgeness related centrality metrics and the Louvain community detection algorithm.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
