Centralities in Complex Networks

Bovet, Alexandre; Makse, Hernán A.

doi:10.1007/978-3-642-27737-5_765-1

Alexandre Bovet² &
Hernán A. Makse³

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2 Citations

Glossary

Adjacency matrix:: The adjacency matrix, A, of a network is a N × N matrix (N = |V|) with element A_ij = 1 if there is an edge from node i to node j and A_ij = 0 otherwise. If the network is weighted, A_ij = w_ij where w_ij ∈ ℝ is the weight associated with the edge between nodes i and j if it exists and A_ij = 0 otherwise. For undirected network, A_ij = A_ji, i.e., A is symmetric.
Connected components:: A connected component of an undirected graph G(V, E) is a subgraph of G, made of a subset of V and all the edges connecting nodes of the subset together, where there exists a path between each pair of nodes. In directed graphs, we differentiate strongly connected components, where there exists a path in both directions between all pairs of nodes, and weakly connected components, where there exists a path in at least one direction between all pairs of nodes.
Degree of a node:: The degree, k_i, of node i in an undirected network is equal to its number of connections, i.e., k_i = ∑_j A_ij. For...

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Acknowledgement

Funding was provided by NIH NIBIB EB028157 and NSF DMR 1945909.

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Authors and Affiliations

Mathematical Institute, University of Oxford, Oxford, UK
Alexandre Bovet
Levich Institute and Physics Department, City College of New York, New York, NY, USA
Hernán A. Makse

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Correspondence to Alexandre Bovet .

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Robert A. Meyers

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Bovet, A., Makse, H.A. (2021). Centralities in Complex Networks. In: Meyers, R.A. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_765-1

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DOI: https://doi.org/10.1007/978-3-642-27737-5_765-1
Received: 15 May 2021
Accepted: 22 May 2021
Published: 03 February 2022
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27737-5
Online ISBN: 978-3-642-27737-5
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