What is global efficiency in graph theory?
The global efficiency of a graph is the average efficiency over all i ≠ j . The concept of global efficiency has been applied to optimization of transportation systems and brain connectivity.
What is meant by global efficiency?
Global efficiency is a measure of the efficiency of distant information transfer in a network and is defined as the inverse of the average characteristic path length between all nodes in the network [67].
What is local efficiency graph theory?
The local efficiency of a particular vertex is the inverse of the average shortest path connecting all neighbors of that vertex.
How do you calculate global efficiency?
Global efficiency for graph G with N vertices is: $$E_{global}(G) = \frac{1}{N(N-1)} \sum_{i \ne j \in G} \frac{1}{d_{ij}}$$ where \(d_{ij}\) is the shortest path length between vertices i and j. Alternatively, global efficiency is equal to the mean of all nodal efficiencies.
Where is productive efficiency on a graph?
In long-run equilibrium for perfectly competitive markets, productive efficiency occurs at the base of the average total cost curve — i.e. where marginal cost equals average total cost — for each good.
What is the purpose of graph theory?
Graph Theory is ultimately the study of relationships . Given a set of nodes & connections, which can abstract anything from city layouts to computer data, graph theory provides a helpful tool to quantify & simplify the many moving parts of dynamic systems.
What is global efficiency in international business?
Ref : Transnational Management [5th edition ] by Bartlett , Ghoshal & Beamish ) (A) Global efficiency : This is about achieving cost economies and revenue maximization through global integration and response to customer needs in varied markets.Companies need to achieve Global integration through deciding on the …
How can we improve network efficiency?
Steps You Can Take to Improve Network Efficiency
- Bring out the cables.
- Clear out network bottlenecks.
- Prioritize operations based on class of service.
- Schedule large workloads for slack times.
- Optimize Your Technology.
- Consider compression.
- Invest in a bandwidth boost.
What is graph theory in network theory?
Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects. In computer science and network science, network theory is a part of graph theory: a network can be defined as a graph in which nodes and/or edges have attributes (e.g. names).
What is the global efficiency of a graph?
The global efficiency of a graph G (with n vertices) is denoted E g l o b ( G) = 1 n ( n − 1) ∑ i ≠ j ∈ ( v i, v j), which is simply the average of the efficiencies over all pairs of vertices. Global efficiency has emerged in a plethora of real world applications including optimization of transportation systems [1], [2], [3], [4],
What is the measure of efficiency between vertices in a graph?
In 2001, Latora and Marchiori introduced the measure of efficiency between vertices in a graph (Latora and Marchiori, 2001). The efficiency between two vertices and is defined to be for all . The global efficiency of a graph is the average efficiency over all .
How do you find the Harary index of global efficiency?
We can use the close relationship between global efficiency and the Harary index, E g l o b ( G) = 2 n ( n − 1) H ( G), to obtain new results. Let H ( G) be the Harary index of a graph G.
How do you find the global efficiency of K M?
We obtain the global efficiency for K m × K n using E g l o b ( K m × P n n − 1) and E g l o b ( K m × C n ⌊ n 2 ⌋).