Detecting Global Bridges in Networks

Slides / Accepted TalkThe identification of nodes occupying important positions in a network structure is crucial for the understanding of the associated real-world system. Usually, betweenness centrality is used to evaluate a node capacity to connect different graph regions. However, we argue here that this measure is not adapted for that task, as it gives equal weight to "local" centers (i.e. nodes of high degree central to a single region) and to "global" bridges, which connect different communities. This distinction is important as the roles of such nodes are different in terms of the local and global organisation of the network structure. In this paper we propose a decomposition of betweenness centrality into two terms, one highlighting the local contributions and the other the global ones. We call the latter bridgeness centrality and show that it is capable to specifically spot out global bridges. In addition, we introduce an effective algorithmic implementation of this measure and demonstrate its capability to identify global bridges in air transportation and scientific collaboration networks

Detecting Global Bridges in Networks

Slides / Accepted TalkThe identification of nodes occupying important positions in a network structure is crucial for the understanding of the associated real-world system. Usually, betweenness centrality is used to evaluate a node capacity to connect different graph regions. However, we argue here that this measure is not adapted for that task, as it gives equal weight to "local" centers (i.e. nodes of high degree central to a single region) and to "global" bridges, which connect different communities. This distinction is important as the roles of such nodes are different in terms of the local and global organisation of the network structure. In this paper we propose a decomposition of betweenness centrality into two terms, one highlighting the local contributions and the other the global ones. We call the latter bridgeness centrality and show that it is capable to specifically spot out global bridges. In addition, we introduce an effective algorithmic implementation of this measure and demonstrate its capability to identify global bridges in air transportation and scientific collaboration networks

Detecting Global Bridges in Networks

Slides / Accepted TalkThe identification of nodes occupying important positions in a network structure is crucial for the understanding of the associated real-world system. Usually, betweenness centrality is used to evaluate a node capacity to connect different graph regions. However, we argue here that this measure is not adapted for that task, as it gives equal weight to "local" centers (i.e. nodes of high degree central to a single region) and to "global" bridges, which connect different communities. This distinction is important as the roles of such nodes are different in terms of the local and global organisation of the network structure. In this paper we propose a decomposition of betweenness centrality into two terms, one highlighting the local contributions and the other the global ones. We call the latter bridgeness centrality and show that it is capable to specifically spot out global bridges. In addition, we introduce an effective algorithmic implementation of this measure and demonstrate its capability to identify global bridges in air transportation and scientific collaboration networks

Dominating sets and ego-centered decompositions in social networks

Our aim here is to address the problem of decomposing a whole network into a minimal number of ego-centered subnetworks. For this purpose, the network egos are picked out as the members of a minimum dominating set of the network. However, to find such an efficient dominating ego-centered construction, we need to be able to detect all the minimum dominating sets and to compare all the corresponding dominating ego-centered decompositions of the network. To find all the minimum dominating sets of the network, we are developing a computational heuristic, which is based on the partition of the set of nodes of a graph into three subsets, the always dominant vertices, the possible dominant vertices and the never dominant vertices, when the domination number of the network is known. To compare the ensuing dominating ego-centered decompositions of the network, we are introducing a number of structural measures that count the number of nodes and links inside and across the ego-centered subnetworks. Furthermore, we are applying the techniques of graph domination and ego=centered decomposition for six empirical social networks.Comment: 17 pages, 7 figure

Structure of Heterogeneous Networks

Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually project such networks unto simple graphs composed of entities of a single type. In the process, they conflate relations between entities of different types and loose important structural information. We develop a mathematical framework that can be used to compactly represent and analyze heterogeneous networks that combine multiple entity and link types. We generalize Bonacich centrality, which measures connectivity between nodes by the number of paths between them, to heterogeneous networks and use this measure to study network structure. Specifically, we extend the popular modularity-maximization method for community detection to use this centrality metric. We also rank nodes based on their connectivity to other nodes. One advantage of this centrality metric is that it has a tunable parameter we can use to set the length scale of interactions. By studying how rankings change with this parameter allows us to identify important nodes in the network. We apply the proposed method to analyze the structure of several heterogeneous networks. We show that exploiting additional sources of evidence corresponding to links between, as well as among, different entity types yields new insights into network structure