Uncovering evolutionary ages of nodes in complex networks

Abstract

In a complex network, different groups of nodes may have existed for different amounts of time. To detect the evolutionary history of a network is of great importance. We present a spectral-analysis based method to address this fundamental question in network science. In particular, we find that there are complex networks in the real-world for which there is a positive correlation between the eigenvalue magnitude and node age. In situations where the network topology is unknown but short time series measured from nodes are available, we suggest to uncover the network topology at the present (or any given time of interest) by using compressive sensing and then perform the spectral analysis. Knowledge of ages of various groups of nodes can provide significant insights into the evolutionary process underpinning the network. It should be noted, however, that at the present the applicability of our method is limited to the networks for which information about the node age has been encoded gradually in the eigen-properties through evolution.

Simulated Evolution of Protein-Protein Interaction Networks with Realistic Topology

“…Our model shows that a protein’s age correlates with certain network properties. Consistent with earlier work [70] – [73] , we find that older proteins tend to be more highly connected. We plotted the ‘age index’ of a protein (the time step at which the protein was introduced) versus its centrality scores.…”

Predicting the sources of an outbreak with a spectral technique

“…In [17] nodes and links of the outbreak network (N = 43) in Figure 4 associate persons, places, objects responsible somehow of the transmission of the infectious agent, therefore the graph do not represents a social network neither approximates a tree. In fact, its performance is poor: 12,21,9,14,17,19, 32, 1 are the DA results, while the actual node origin is 1, immediately after we have node 2, 3, 4, 5 (representing places).…”

“…The origin is node 1 (red dotted circle), then we have node 2, 3, 4, 5, 6 (that represents places instead of persons). Results from DA: 12,21,9,14,17,19, 32, 1. The random guessing in this case obtains the same performance of DA in the 17% of the 10 6 runs (ordering is not considered).…”

Node Seniority Ranking in Networks

“…Zhu (1) instead has developed a deterministic spectral strategy based only on the topology of the network (solving de facto an inverse problem) at the same computational cost O(N 3 ), applying his method to the Santa Fè co-authorship social network (3) and to the protein-protein interaction network.…”

“…3) for 1000, 2500, 10000 nodes. Locating the sources in this kind of graph is easy because of the preferential attachment rule sets a strong correlation with the degree (1). The ECI procedure, in fact, finds the four sources (nodes 1, 2, 3, 4) within the first six positions of the calculated ranking (2, 4, 1, 21, 17, 3), adding two false positive nodes, 21 and 17; better results with a BA 2500 nodes graph: the four sources (nodes 1, 2, 3, 4) are within the first five positions of the ranking (4, 6, 3, 2, 1) adding as a false positive only node 6, and finally for a BA graph of 10000 nodes we obtain all the sources (2, 3, 1, 4) with no errors.…”