The increasing availability of large network datasets derived from high-throughput experiments requires the development of tools to extract relevant information from biological networks, and the development of computational methods capable of detecting qualitative and quantitative changes in the topological properties of biological networks is of critical relevance. We introduce the notions of node and as measures of the reciprocal influence between nodes within a network. We examine the theoretical significance of these new, centrality-based, measures by characterizing the topological relationships between nodes and groups of nodes. Node interference analysis allows topologically determining the context of functional influence of single nodes. Conversely, the node robustness analysis allows topologically identifying the nodes having the highest functional influence on a specific node. A new Cytoscape plug-in calculating these measures was developed and applied to a protein-protein interaction network specifically regulating integrin activation in human primary leukocytes. Notably, the functional effects of compounds inhibiting important protein kinases, such as SRC, HCK, FGR and JAK2, are predicted by the interference and robustness analysis, are in agreement with previous studies and are confirmed by laboratory experiments. The interference and robustness notions can be applied to a variety of different contexts, including, for instance, the identification of potential side effects of drugs or the characterization of the consequences of genes deletion, duplication or of proteins degradation, opening new perspectives in biological network analysis.