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It measures the diversity of self-avoiding walks which start from a given node. A walk on a network is a sequence of adjacent vertices; a self-avoiding walk visits (lists) each vertex at most once. The original work used simulated walks of length 60 to characterize the network of urban streets in a Brazilian city. [6]
A simple social network: the nodes represent people or actors and the edges between nodes represent some relationship between actors. Katz centrality computes the relative influence of a node within a network by measuring the number of the immediate neighbors (first degree nodes) and also all other nodes in the network that connect to the node under consideration through these immediate neighbors.
The number next to each node is the distance from that node to the square red node as measured by the length of the shortest path. The green edges illustrate one of the two shortest paths between the red square node and the red circle node. The closeness of the red square node is therefore 5/(1+1+1+2+2) = 5/7.
Percolation centrality is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.
In graph theory, eigenvector centrality (also called eigencentrality or prestige score [1]) is a measure of the influence of a node in a connected network.Relative scores are assigned to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.
All these models had one thing in common: they all predicted very short average path length. [1] The average path length depends on the system size but does not change drastically with it. Small world network theory predicts that the average path length changes proportionally to log n, where n is the number of nodes in the network.
Transmission delay is a function of the packet's length and has nothing to do with the distance between the two nodes. This delay is proportional to the packet's length in bits. It is given by the following formula: = / seconds. where: is the transmission delay in seconds;
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]