This paper introduces a new measure of centrality, denoted as \( C_F \), which is based on network flows and is designed to overcome the limitations of existing measures like \( C_B \). The key differences between \( C_F \) and \( C_B \) are: 1. **Applicability to Valued and Non-Valued Graphs**: \( C_F \) is defined for both valued and non-valued graphs, making it more versatile for various network datasets. 2. **Computation Based on All Independent Paths**: Unlike \( C_B \), which focuses on geodesic paths, \( C_F \) considers all independent paths between pairs of points in the network. The paper begins by reviewing the concept of centrality from two different perspectives: proximity and betweenness. It then introduces the \( C_B \) family of measures, which are based on graph theory and assume that information flows only along the shortest paths. However, these measures have limitations, such as being restricted to simple graphs and focusing only on geodesic paths. To address these limitations, the authors propose \( C_F \), which uses Ford and Fulkerson's model of network flows. In this model, the capacity of an edge represents the strength of the social linkage between two individuals, and information flows along these channels. The measure \( C_F \) calculates the degree to which a point \( x_i \) is necessary for the maximum flow between other points by summing the maximum flows that pass through \( x_i \). The paper also discusses the normalization and centralization of \( C_F \) measures, similar to \( C_B \). It provides a detailed example to illustrate how \( C_F \) is calculated and compared with \( C_B \). The authors conclude by highlighting the advantages of \( C_F \) over \( C_B \), particularly in handling valued data and considering all independent paths, making it more realistic for depicting network structure.This paper introduces a new measure of centrality, denoted as \( C_F \), which is based on network flows and is designed to overcome the limitations of existing measures like \( C_B \). The key differences between \( C_F \) and \( C_B \) are: 1. **Applicability to Valued and Non-Valued Graphs**: \( C_F \) is defined for both valued and non-valued graphs, making it more versatile for various network datasets. 2. **Computation Based on All Independent Paths**: Unlike \( C_B \), which focuses on geodesic paths, \( C_F \) considers all independent paths between pairs of points in the network. The paper begins by reviewing the concept of centrality from two different perspectives: proximity and betweenness. It then introduces the \( C_B \) family of measures, which are based on graph theory and assume that information flows only along the shortest paths. However, these measures have limitations, such as being restricted to simple graphs and focusing only on geodesic paths. To address these limitations, the authors propose \( C_F \), which uses Ford and Fulkerson's model of network flows. In this model, the capacity of an edge represents the strength of the social linkage between two individuals, and information flows along these channels. The measure \( C_F \) calculates the degree to which a point \( x_i \) is necessary for the maximum flow between other points by summing the maximum flows that pass through \( x_i \). The paper also discusses the normalization and centralization of \( C_F \) measures, similar to \( C_B \). It provides a detailed example to illustrate how \( C_F \) is calculated and compared with \( C_B \). The authors conclude by highlighting the advantages of \( C_F \) over \( C_B \), particularly in handling valued data and considering all independent paths, making it more realistic for depicting network structure.