Improving C2 Effectiveness Based on Robust Connectivity

Introduction

The application of network theory enables us to investigate alternatives to the traditional hierarchical organizations of Command and Control (C2) processes and systems. Traditional hierarchical organizations were the result of centralized command and control cultures and the significant costs, both in time and money, of distributing the necessary information to enable sound decision-making. The increased desire for peer-to-peer negotiation and self-synchronization and the incredible reduction in these costs during the past decade has made non-hierarchical organizations viable alternatives. It also introduced a significant challenge: what should we measure to determine which organization can be more effective?

The effectiveness of a C2 network is more than just the sum of its nodes and arcs, which can be measured by the link-to-node ratio (l/N). A maximally-connected network, where every node is connected to every other node (i.e., l = (N-1)!), not only remains prohibitive in monetary cost; it is undesirable due to the inability of a node to manage or process the overwhelming information flow represented by the arcs. However, a minimally-connected network may not be desirable due to either insufficient capability or capacity or an increased vulnerability of the network. Additionally, the link-to-node ratio metric cannot discriminate between alternative network organizations that have the same numbers of nodes and links, but differ solely in their arrangement. The mere counting of a link does not account for its significance, or lack thereof.

The degree distribution metric is a measurement of whether the number of links connected to each node is uniformly distributed throughout a network. Adaptive, complex networks have a small number of highly connected nodes (i.e., a skewed degree distribution). Such highly connected nodes can be clustered together or can be distanced from each other, and is expressed as a clustering coefficient calculated from the proportion of a node’s direct neighbors that are also direct neighbors of each other. This represents a measurement of a network’s cohesion and self-synchronization. The characteristic path length is a related metric, and is measured as the median of the mean of the lengths of all the shortest paths in the network. While these metrics begin to account for link significance, they are insufficient in discriminating between network configurations that vary in the placement of just a single link.

Jain and Krishna (2002) introduced the relationship between the Perron-Frobenius Eigenvalue (λ_PFE) of a graph and its autocatalytic sets, and used graph topology to study various network dynamics. Cares (2005) employed a similar approach to describe combat (or competition) between distributed, networked forces or organizations. His Information Age Combat Model (IACM) focused on the λ_PFE as a measure of the ability of a network to produce combat power. Cares proposed that the greater the value of the λ_PFE, the greater the effectiveness of the organization of that networked force.

Deller, et al (2009, 2012) confirmed this proposal by constructing an agent-based simulation that enabled networked organizations to compete against each other in the context of Cares’ IACM. The results of the agent-based simulation indicated that the value of the λ_PFE was a significant measurement of the performance of a networked force. However, the effectiveness of the λ_PFE measurement was dependent on the existence of unique λ_PFE values for the configurations under consideration. When alternative organizations had a shared λ_PFE value, additional measurements were required to enable discrimination. Of the additional metrics considered, robustness proved the most effective in improving the value of the λ_PFE as a quantifiable metric of network performance. Ultimately, the best indicator of network effectiveness was a metric that combined both the λ_PFE and robustness values.