Documentation branch

brainconn/centrality/centrality.py

@@ -7,13 +7,39 @@
 from ..distance import reachdist
 from ..utils import invert
 
+def Degree_centrality (G):
+    """
+    Degree centrality, is the simplest measure of centrality. It assumes
+    that no nodes with many connections exert more influence over network.
+    However, the limitation of degree centrality is that all connections
+    are treated as same strength.
+
+    """
+
+def Delta_centrality (G):
+    """
+    Another way of thinking about centrality is that it does not depend
+    on either degree, closeness or betweenness but is based on the effect
+    of the removal of a node has on the structure and function of the rest
+    of the network.
 
-def betweenness_bin(G):
+    The intuition behind this measure is that inactivation of nodes will
+    exert a disproportionate impact on remaining network elements.
+
+    Delta centrality is closely related to analysis of network robustness.
+
+    Used to creat putative scaffold. Refer to Sporns (2016) paper to see an
+    example of structural scaffold of human brain.
+    """
+
+def betweenness(G):
     """
     Node betweenness centrality is the fraction of all shortest paths in
     the network that contain a given node. Nodes with high values of
     betweenness centrality participate in a large number of shortest paths.
 
+
+
     Parameters
     ----------
     A : NxN :obj:`numpy.ndarray`
@@ -26,6 +52,10 @@ def betweenness_bin(G):
     -----
     Betweenness centrality may be normalised to the range [0,1] as
     BC/[(N-1)(N-2)], where N is the number of nodes in the network.
+
+    Betweeness centrality assumes that the information is routed
+    along the shortest paths which may not be an appropriate assumption
+    in case information transmission in brain.
     """
     G = np.array(G, dtype=float)  # force G to have float type so it can be
     # compared to float np.inf
@@ -185,7 +215,7 @@ def entropy(w_):
     return Hpos, Hneg
 
 
-def edge_betweenness_bin(G):
+def edge_betweenness(G):
     """
     Edge betweenness centrality is the fraction of all shortest paths in
     the network that contain a given edge. Edges with high values of
@@ -341,6 +371,13 @@ def eigenvector_centrality_und(CIJ):
     node i is equivalent to the ith element in the eigenvector
     corresponding to the largest eigenvalue of the adjacency matrix.
 
+    Eigenvector centrality is based on the notion that the given node is highly
+    central if its' neighbors also share the same property. Howveer, it does not
+    account for the disparity in degree of a node with respect to its'
+    neighbours. This has different implications depending on the networks'
+    assortavity and the tendency of a node to be connected to nodes with
+    similar degrees (Joyce, 2010)
+
     Parameters
     ----------
     CIJ : NxN :obj:`numpy.ndarray`
@@ -655,6 +692,9 @@ def module_degree_zscore(W, ci, flag=0):
 
 def pagerank_centrality(A, d, falff=None):
     """
+    Interesting fact: It is used to rank websites in the results of Google
+    search engine.
+
     The PageRank centrality is a variant of eigenvector centrality. This
     function computes the PageRank centrality of each vertex in a graph.
 
@@ -817,3 +857,16 @@ def subgraph_centrality(CIJ):
     # compute eigenvector centr.
     Cs = np.real(np.dot(vecs * vecs, np.exp(vals)))
     return Cs  # imaginary part from precision error
+
+def Leverage_centrality:
+    """
+    This concept considers the centrality of the node depending on whether
+    its neighbour rely on the node for information
+
+    leverage centrality does not assume shortest path or in a serial fashion.
+    It focuses on disparity in node degrees to quantify information flow
+    locally.
+
+    For further information on utitlity of leverage centrality in the
+    brain network refer to Joyce (2010)
+    """