  We introduce a new centrality measure that characterizes the participation of
each node in all subgraphs in a network. Smaller subgraphs are given more
weight than larger ones, which makes this measure appropriate for
characterizing network motifs. We show that the subgraph centrality (SC) can be
obtained mathematically from the spectra of the adjacency matrix of the
network. This measure is better able to discriminate the nodes of a network
than alternate measures such as degree, closeness, betweenness and eigenvector
centralities. We study eight real-world networks for which SC displays useful
and desirable properties, such as clear ranking of nodes and scale-free
characteristics. Compared with the number of links per node, the ranking
introduced by SC (for the nodes in the protein interaction network of S.
cereviciae) is more highly correlated with the lethality of individual proteins
removed from the proteome.
