page_title: Dependency network
section_title: Importance
hierarchical_section_title: Dependency network / Importance
caption_attribution_description: English: Dependency Network of specific antibodies activity, measured for a group of mothers. Panel (a) presents the Dependency Network, and panel (b) the standard correlation network. Reproduction from Madi et al., Chaos 21, 016109 (2011)
context_page_description: The dependency network approach provides a system level analysis of the activity and topology of directed networks. The approach extracts causal topological relations between the network's nodes, and provides an important step towards inference of causal activity relations between the network nodes. This methodology has originally been introduced for the study of financial data, it has been extended and applied to other systems, such as the immune system, and semantic networks.
  In the case of network activity, the analysis is based on partial correlations, which are becoming ever more widely used to investigate complex systems. In simple words, the partial correlation is a measure of the effect of a given node, say j, on the correlations between another pair of nodes, say i and k. Using this concept, the dependency of one node on another node, is calculated for the entire network. This results in a directed weighted adjacency matrix, of a fully connected network. Once the adjacency matrix has been constructed, different algorithms can be used to construct the network, such as a threshold network, Minimal Spanning Tree, Planar Maximally Filtered Graph, and others.
context_section_description: The partial correlation based dependency network is a class of correlation network, capable of uncovering hidden relationships between its nodes.
  This original methodology was first presented at the end of 2010, published in PLoS ONE. They quantitatively uncovered hidden information about the underlying structure of the U.S. stock market, information that was not present in the standard correlation networks. One of the main results of this work is that for the investigated time period (2001–2003), the structure of the network is dominated by companies belonging to the financial sector, which are the hubs in the dependency network. Thus, they were able for the first time to quantitatively show the dependency relationships between the different economic sectors. Following this work, the dependency network methodology has been applied to the study of the immune system, and semantic networks. As such, this methodology is applicable to any complex system.
caption: Dependency Network of specific antibodies activity, measured for a group of mothers. Panel (a) presents the dependency network, and panel (b) the standard correlation network. Reproduction from Madi et al., Chaos 21, 016109 (2011)
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